Report: London Property Values, Consumer Surveys, and Market Trends
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AI Summary
This report investigates the trends in London property values, focusing on consumer behavior, particularly among mortgage investors. It examines the impact of economic factors, such as supply and demand, on house prices and affordability. The report analyzes consumer survey data from 2010 onwards, revealing investor sentiment and expectations regarding homeownership, interest rates, and economic growth. It also explores the challenges faced by potential homebuyers, including financial preparedness, mortgage stress tests, and the influence of government policies. The analysis covers housing market trends, including different measures of house prices from various sources like the Office for National Statistics (ONS) and Land Registry, and their methodologies. The report highlights the impact of mortgage lending regulations and the role of parental financial support. It concludes by discussing the effects of stress tests on potential homebuyers, changes in homeownership rates, and the long-term implications of these trends on the London housing market. The report also examines the attitudes towards mortgage stress tests and the impact of federal policies, which have made it difficult for potential buyers to access mortgage financing.

Introduction
The objective of this investigation is to determine the trend in property values in London and
how they typically change. The report will focus more on the survey of the consumer who are
largely investing on property mortgages. The investigation focuses on the housing market in
London, which presently is recording a massive and rapid transition. The clear picture is depicted
on the importance processes that will aid the market in either selling or buying homes
(Chatterjee, and Eyigungor, 2009), while considering the level of house prices changes being
realistic, and likely long-term consequences of the price of houses London inflation. The paper
concentrates more on the cost of homes and housing in terms of economic states in London
(Landes and Posner, 2009). Based on economic term the price of houses in equilibrium is fixed
by balancing the supply and demand. In the case where there is persistent respond fail to prices
that are high, or where prices are determined by factors rather than the fundamental housing
need, the buying desire and ability to pay, the price of houses may be considered overvalued or
unaffordable. The consequences of this projected on the wages and business cost and also the
increment in the risks to stability of macroeconomic. The affordability is defined as the
relationship that exists between the cost of market determined of housing and the pay ability in
terms of economic context. The context is not related to home affordability which lies within
social rent (Angelopoulos, Philippopoulos and Vassilatos, 2009), affordable rent and
intermediate housing, where the housing needs do not meet the criteria of the market. The house
budget may be beyond the limit of some household, which critically place some of the
householders to have difficulty to pay the houses and blocking them from home ownership.
Inequality can also be experienced when the prices of the houses are high, and the concentration
related to wealth among the home owners, across the present generation.
The objective of this investigation is to determine the trend in property values in London and
how they typically change. The report will focus more on the survey of the consumer who are
largely investing on property mortgages. The investigation focuses on the housing market in
London, which presently is recording a massive and rapid transition. The clear picture is depicted
on the importance processes that will aid the market in either selling or buying homes
(Chatterjee, and Eyigungor, 2009), while considering the level of house prices changes being
realistic, and likely long-term consequences of the price of houses London inflation. The paper
concentrates more on the cost of homes and housing in terms of economic states in London
(Landes and Posner, 2009). Based on economic term the price of houses in equilibrium is fixed
by balancing the supply and demand. In the case where there is persistent respond fail to prices
that are high, or where prices are determined by factors rather than the fundamental housing
need, the buying desire and ability to pay, the price of houses may be considered overvalued or
unaffordable. The consequences of this projected on the wages and business cost and also the
increment in the risks to stability of macroeconomic. The affordability is defined as the
relationship that exists between the cost of market determined of housing and the pay ability in
terms of economic context. The context is not related to home affordability which lies within
social rent (Angelopoulos, Philippopoulos and Vassilatos, 2009), affordable rent and
intermediate housing, where the housing needs do not meet the criteria of the market. The house
budget may be beyond the limit of some household, which critically place some of the
householders to have difficulty to pay the houses and blocking them from home ownership.
Inequality can also be experienced when the prices of the houses are high, and the concentration
related to wealth among the home owners, across the present generation.
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Consumer Sentiment
The consumer survey research since 2010 found out that the house investors in London are more
comfortable in regard to the choices they made. Tabe1 shows the survey carried out
Consumer responses to survey questions
2010 2011 2012 2013 2014 2015 201
6
2017 2018
The low interest rate is aimed
at ensuring many individuals
become homeowners
6.9 7.1 7.0 7.0 7.0 6.8 7.0 7.2 6.9
Regret on the consumer size
of mortgages
3.9 4.0 3.9 3.8 3.9 3.7 3.6 3.7 3.5
More individual are ready to
own home if the prices to
purchase the houses are
lowered
6.5 6.7 6.7 6.9 7.0 6.9 7.0 7.1 7.1
The investment on real estate
in London is good ventures
to investors
7.1 7.3 7.3 7.4 7.4 7.4 7.2 7.2 7.2
The economy is expected to
rise in the next 12 months if
more housing are acquired
through mortgages
N/A 6.0 6.1 6.4 6.3 6.2 6.0 6.3 6.1
Mortgages are good debt to
service.
N/A 7.1 7.1 7.2 7.2 7.1 7.0 7.0 6.8
Consequently, as from 2010, three queries have been raised about expectations: • previously,
positive feedback have been received from a statement “Now is a good or bad time to buy a
home/condominium in my community”. For the case of spring (and fall for the past year),
feedbacks have fallen to neutrality.
•Consumer expectations on the growth of house prices are relatively similar to prior years;
however, sharp differences are recorded across the country.
• Consumers are projecting an increase in interest rates. As viewed in the past, the feedback
indicates a reflection of recent happenings and are not an indicator of what will happen. The
survey also included people who at the moment of research did not own homes, they were asked
about the reason behind not owning. The feedbacks of young Londoners (described as those aged
35 years and below) show:
• Most of them mentioned lack of financial preparedness as the major reason (mostly requiring
time to save for a down payment).
The consumer survey research since 2010 found out that the house investors in London are more
comfortable in regard to the choices they made. Tabe1 shows the survey carried out
Consumer responses to survey questions
2010 2011 2012 2013 2014 2015 201
6
2017 2018
The low interest rate is aimed
at ensuring many individuals
become homeowners
6.9 7.1 7.0 7.0 7.0 6.8 7.0 7.2 6.9
Regret on the consumer size
of mortgages
3.9 4.0 3.9 3.8 3.9 3.7 3.6 3.7 3.5
More individual are ready to
own home if the prices to
purchase the houses are
lowered
6.5 6.7 6.7 6.9 7.0 6.9 7.0 7.1 7.1
The investment on real estate
in London is good ventures
to investors
7.1 7.3 7.3 7.4 7.4 7.4 7.2 7.2 7.2
The economy is expected to
rise in the next 12 months if
more housing are acquired
through mortgages
N/A 6.0 6.1 6.4 6.3 6.2 6.0 6.3 6.1
Mortgages are good debt to
service.
N/A 7.1 7.1 7.2 7.2 7.1 7.0 7.0 6.8
Consequently, as from 2010, three queries have been raised about expectations: • previously,
positive feedback have been received from a statement “Now is a good or bad time to buy a
home/condominium in my community”. For the case of spring (and fall for the past year),
feedbacks have fallen to neutrality.
•Consumer expectations on the growth of house prices are relatively similar to prior years;
however, sharp differences are recorded across the country.
• Consumers are projecting an increase in interest rates. As viewed in the past, the feedback
indicates a reflection of recent happenings and are not an indicator of what will happen. The
survey also included people who at the moment of research did not own homes, they were asked
about the reason behind not owning. The feedbacks of young Londoners (described as those aged
35 years and below) show:
• Most of them mentioned lack of financial preparedness as the major reason (mostly requiring
time to save for a down payment).

• A small section described negative attitude towards owning a home as a reason. They described
homeownership as a bad investment and stressful. Many young people are still interested in
buying homes. For those between 25 to 34 years, three-quarters project and hopes to buy a home
in a period not exceeding five years. The question at hand is whether they have the ability to buy
the home.
• Determining factors are income, employment, confidence on their economic prospects and
access to down payments. • Similarly, market conditions such as ability to find alternatives that
meet their reasonable needs and wishes at an affordable cost.
• Ability to obtain mortgage financing even when personal circumstances and market conditions
are favorable is essential. Policies set by the federal government are making it hard for potential
buyers to access mortgage financing. For those potential homeowners who are adversely affected
by the federal government policies, the possible solutions involve making large down payments
and potentially lowering their expectations. From the research results, 18% of potential
homebuyers will fail the threshold of a stress test. For those who fail the stress test, an average of
$28,750 is the required adjustment. For an estimate of 120,000 potential homebuyers, the
required adjustments would be relatively small for most. On contrary, about 30,000 to 40,000 per
year are estimated to undergo larger effects and would need cough out larger down payments
leading to extended delays.
The primary source of source for down payments is personal savings estimated at over half of the
total funds improved by funds obtained from the buyers’ RRSPs estimated at a tenth of total
funds. Parents also contribute to the down payments. The impact of funds from parents is
increasingly important but falls less than a fifth of total down payments. Financial institutions
also play a big role by provision of loans. Obtaining down payments through borrowing has been
made more difficult after the revision of mortgage lending regulations. This means that the
potential buyers are required to increase the amount they put down making them less able to
fulfill. This results to a lengthy period of accumulating funds hence delaying buying of the
homes. A portion of first-time buyers will require help from their parents where in most cases
they obtain. This insinuates that rationing will take effect in the housing market (Piazzesi and
Schneider, 2009). The help obtained from parents will determine the ability of the buyers’ to
purchase the homes. The income and personal prospect of the prospective buyers will eventually
be less important as compared to the ability and willingness of parents to donate or lend funds to
their children. The proportion of homeownership in London has reduced from 69% in 2011 to
68% in 2016 brought about by increased difficulty in saving for down payments. Increasing
hurdles brought but federal government policies will top up on the ownership rate. From history,
it is more advantageous to own a home in London than to rent. No concrete evidence shows that
there is a change. Hence, federal government policies on mortgages suppress home ownership
homeownership as a bad investment and stressful. Many young people are still interested in
buying homes. For those between 25 to 34 years, three-quarters project and hopes to buy a home
in a period not exceeding five years. The question at hand is whether they have the ability to buy
the home.
• Determining factors are income, employment, confidence on their economic prospects and
access to down payments. • Similarly, market conditions such as ability to find alternatives that
meet their reasonable needs and wishes at an affordable cost.
• Ability to obtain mortgage financing even when personal circumstances and market conditions
are favorable is essential. Policies set by the federal government are making it hard for potential
buyers to access mortgage financing. For those potential homeowners who are adversely affected
by the federal government policies, the possible solutions involve making large down payments
and potentially lowering their expectations. From the research results, 18% of potential
homebuyers will fail the threshold of a stress test. For those who fail the stress test, an average of
$28,750 is the required adjustment. For an estimate of 120,000 potential homebuyers, the
required adjustments would be relatively small for most. On contrary, about 30,000 to 40,000 per
year are estimated to undergo larger effects and would need cough out larger down payments
leading to extended delays.
The primary source of source for down payments is personal savings estimated at over half of the
total funds improved by funds obtained from the buyers’ RRSPs estimated at a tenth of total
funds. Parents also contribute to the down payments. The impact of funds from parents is
increasingly important but falls less than a fifth of total down payments. Financial institutions
also play a big role by provision of loans. Obtaining down payments through borrowing has been
made more difficult after the revision of mortgage lending regulations. This means that the
potential buyers are required to increase the amount they put down making them less able to
fulfill. This results to a lengthy period of accumulating funds hence delaying buying of the
homes. A portion of first-time buyers will require help from their parents where in most cases
they obtain. This insinuates that rationing will take effect in the housing market (Piazzesi and
Schneider, 2009). The help obtained from parents will determine the ability of the buyers’ to
purchase the homes. The income and personal prospect of the prospective buyers will eventually
be less important as compared to the ability and willingness of parents to donate or lend funds to
their children. The proportion of homeownership in London has reduced from 69% in 2011 to
68% in 2016 brought about by increased difficulty in saving for down payments. Increasing
hurdles brought but federal government policies will top up on the ownership rate. From history,
it is more advantageous to own a home in London than to rent. No concrete evidence shows that
there is a change. Hence, federal government policies on mortgages suppress home ownership
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and are coupling up to increase financial stress experienced by younger generation living in
London (Chiquier, 2009).
Attitudes Towards the Mortgage Stress Tests
A rough estimate of 100,000 Londoners have been barred from purchasing a home as a result
stress testing needed by the government even if in real sense, they have the financial power to
buy as per their actual circumstances. As a repercussion, few Londoners have been exposed to
the effects of the stress tests hence are less knowledgeable on the same. Prospective home
owners are also expected to have some knowledge and knowhow about the potential effects. This
version of our buyer study examined assumptions regarding impacts of the pressure tests. We
found that around 33% (32%) of buyers would expect huge negative effects on their capacity to
purchase a home in their favored neighborhood (8 to 10 on a 10-point scale). A comparative
extent (29%) would expect insignificant effects (1 to 3 out of 10), and 39% expect moderate
effects (4 to 7 out of 10). In any case, looking all the more barely, at individuals who are not as
of now mortgage holders but rather hope to purchase in the following five years, more than one-
half (54%) expect huge negative effects, and 35% expect moderate effects. Simply 11% expect
immaterial effects.
The discoveries made during survey are in line with what occurred in housing markets: up to this
far in the year, London’s resale market activity has reduced by 13% in comparison with the
previous year and by 17% in comparison with 2016. This decrease is caused by modest rises in
interest rates levied on mortgages and to provincial government policies aimed at discouraging
non-residents from owning homes. The primary cause of slowdown is the increased difficulty in
obtaining mortgage financing (Loutskina and Strahan, 2009).
Housing Market Trends
There are various proportions of house costs, which can offer ascent to various evaluations of the
dimension of house costs and how they are changing after some time. These reflect contrasts in
the hidden information and procedures for their accumulation. There are two 'official'
proportions of house value levels in the UK:
1) The Office for National Statistics (ONS) house price data: In light of an agent test of broad
home mortgage loaning through the Regulated Mortgage Survey of the Council of Mortgage
Lenders18.
2) Land Registry price paid data: In light of a total enlist of every single private deal at full
market value19 in England and Wales. Different datasets are likewise created by Nationwide and
Halifax dependent on their own home loan endorsements, regardless of whether these outcome in
real buys. Moreover, correlation sites, for example, Rightmove.com and Zoopla deliver
London (Chiquier, 2009).
Attitudes Towards the Mortgage Stress Tests
A rough estimate of 100,000 Londoners have been barred from purchasing a home as a result
stress testing needed by the government even if in real sense, they have the financial power to
buy as per their actual circumstances. As a repercussion, few Londoners have been exposed to
the effects of the stress tests hence are less knowledgeable on the same. Prospective home
owners are also expected to have some knowledge and knowhow about the potential effects. This
version of our buyer study examined assumptions regarding impacts of the pressure tests. We
found that around 33% (32%) of buyers would expect huge negative effects on their capacity to
purchase a home in their favored neighborhood (8 to 10 on a 10-point scale). A comparative
extent (29%) would expect insignificant effects (1 to 3 out of 10), and 39% expect moderate
effects (4 to 7 out of 10). In any case, looking all the more barely, at individuals who are not as
of now mortgage holders but rather hope to purchase in the following five years, more than one-
half (54%) expect huge negative effects, and 35% expect moderate effects. Simply 11% expect
immaterial effects.
The discoveries made during survey are in line with what occurred in housing markets: up to this
far in the year, London’s resale market activity has reduced by 13% in comparison with the
previous year and by 17% in comparison with 2016. This decrease is caused by modest rises in
interest rates levied on mortgages and to provincial government policies aimed at discouraging
non-residents from owning homes. The primary cause of slowdown is the increased difficulty in
obtaining mortgage financing (Loutskina and Strahan, 2009).
Housing Market Trends
There are various proportions of house costs, which can offer ascent to various evaluations of the
dimension of house costs and how they are changing after some time. These reflect contrasts in
the hidden information and procedures for their accumulation. There are two 'official'
proportions of house value levels in the UK:
1) The Office for National Statistics (ONS) house price data: In light of an agent test of broad
home mortgage loaning through the Regulated Mortgage Survey of the Council of Mortgage
Lenders18.
2) Land Registry price paid data: In light of a total enlist of every single private deal at full
market value19 in England and Wales. Different datasets are likewise created by Nationwide and
Halifax dependent on their own home loan endorsements, regardless of whether these outcome in
real buys. Moreover, correlation sites, for example, Rightmove.com and Zoopla deliver
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proportions of promoted asking costs and evaluated costs separately, while the Royal Institution
of Chartered Surveyors (RICS) produces a main estimation pointer of conditions in the UK
private deals markets, in view of new purchaser enquiries. Main estimation pointers can be
utilized to foretell the expected trends in the market. This is on the grounds that they defeat the
time slacks related with the property pursuit and offer process, having a home loan endorsed, an
exchange finished and enlisted with the Land Registry20. In any case, since they depend on an
agent test or thorough enroll of real house deals, the two authority information sources give an
increasingly solid proportion of the normal cost of house deals at a specific point in time. Land
Registry information is an especially rich wellspring of information on the 'going market sector
rate' of lodging at a given time as it can likewise give data at borough level. It likewise
incorporates exchanges dependent on money buys and additionally those sponsored by home
loan back, while the ONS information just catches buys financed by UK mortgages21. ONS
information rather profits by a more extravagant time arrangement, giving information on house
costs by UK region back to 1969. The Land Registry information, however accessible at an
increasingly definite dimension, goes back just to the extent 1996. Since house value changes
after some time might be influenced by the quality and attributes of the supply of housing
accessible for procurement, the ONS, Land Registry, Nationwide and Halifax each deliver their
very own House Price Index (HPI) (De Vries, de Haan, Van der Wal and Mariën, 2009). The
variations in the index contrasted with a year sooner is utilized to tell whether costs are rising or
falling. House prices indices tend to disengage fluctuations in prices from changes in in the blend
of houses sold within certain time periods. No material is able to take liability for fluctuations in
the quality of house stock brought about by improvements or decline in homes. The ONS,
Nationwide and Halifax HPIs adjust for the changing mix of properties made available in any
given period (in terms of size, number of bedrooms and a range of other characteristics) to
measure the price of an ‘average house’22. The corresponding Land Registry HPI is instead a
form of ‘repeat sales regression’ index which insinuates that it offers the measurement of average
price fluctuation in repeat purchases on similar properties. Hence, it regulates the differences in
the properties of each house that is resold. These records are especially applicable to
understanding the incentive to those holding property at a specific minute in time, and the
estimation of the lodging stock that might be accessible available to be purchased later on. While
there are a scope of sources accessible, the Land Registry information gives the most precise
picture of costs paid in the lodging market. In any case, in spite of the fact that it is less extensive
in its inclusion of exchanges and ostensibly less thorough in its blend change as a result23, the
ONS HPI goes about as a valuable measure at the genuine cost of house deals for every UK area
over longer timeframes. The option datasets depend on promoted, rather than the acknowledged
cost of property exchanges. The following segment sets out the ongoing patterns in London
house costs, and places these with regards to the national picture and past financial cycles
(Taylor, 2007).
of Chartered Surveyors (RICS) produces a main estimation pointer of conditions in the UK
private deals markets, in view of new purchaser enquiries. Main estimation pointers can be
utilized to foretell the expected trends in the market. This is on the grounds that they defeat the
time slacks related with the property pursuit and offer process, having a home loan endorsed, an
exchange finished and enlisted with the Land Registry20. In any case, since they depend on an
agent test or thorough enroll of real house deals, the two authority information sources give an
increasingly solid proportion of the normal cost of house deals at a specific point in time. Land
Registry information is an especially rich wellspring of information on the 'going market sector
rate' of lodging at a given time as it can likewise give data at borough level. It likewise
incorporates exchanges dependent on money buys and additionally those sponsored by home
loan back, while the ONS information just catches buys financed by UK mortgages21. ONS
information rather profits by a more extravagant time arrangement, giving information on house
costs by UK region back to 1969. The Land Registry information, however accessible at an
increasingly definite dimension, goes back just to the extent 1996. Since house value changes
after some time might be influenced by the quality and attributes of the supply of housing
accessible for procurement, the ONS, Land Registry, Nationwide and Halifax each deliver their
very own House Price Index (HPI) (De Vries, de Haan, Van der Wal and Mariën, 2009). The
variations in the index contrasted with a year sooner is utilized to tell whether costs are rising or
falling. House prices indices tend to disengage fluctuations in prices from changes in in the blend
of houses sold within certain time periods. No material is able to take liability for fluctuations in
the quality of house stock brought about by improvements or decline in homes. The ONS,
Nationwide and Halifax HPIs adjust for the changing mix of properties made available in any
given period (in terms of size, number of bedrooms and a range of other characteristics) to
measure the price of an ‘average house’22. The corresponding Land Registry HPI is instead a
form of ‘repeat sales regression’ index which insinuates that it offers the measurement of average
price fluctuation in repeat purchases on similar properties. Hence, it regulates the differences in
the properties of each house that is resold. These records are especially applicable to
understanding the incentive to those holding property at a specific minute in time, and the
estimation of the lodging stock that might be accessible available to be purchased later on. While
there are a scope of sources accessible, the Land Registry information gives the most precise
picture of costs paid in the lodging market. In any case, in spite of the fact that it is less extensive
in its inclusion of exchanges and ostensibly less thorough in its blend change as a result23, the
ONS HPI goes about as a valuable measure at the genuine cost of house deals for every UK area
over longer timeframes. The option datasets depend on promoted, rather than the acknowledged
cost of property exchanges. The following segment sets out the ongoing patterns in London
house costs, and places these with regards to the national picture and past financial cycles
(Taylor, 2007).

Table 1: Median house prices and house price trends in London, England and Wales, 1996-2014
Median house prices, pounds Compound growth rate, %
1996 2007 2009 2014 1996-
2007
2007-
2009
2009-
2014
England
and
Wales
57,000 176,000 169,000 192,000 11 -2 3
London 77,000 265,000 250,000 364,000 12 -3 8
Inner
London
87,000 313,000 323,000 462,000 12 2 7
Outer
London
74,000 249,000 235,000 315,000 12 -3 6
The figures represented in table 1 potrays a large variation across various parts of London. In
2014, the going market rate was high in central boroughs with a relative high price of £857,000
and £1,198,000 in Westminster and Kensington respectively as per the records provided by Land
Registry. In Barking and Dagenham, the mean price for purchasing a house was £215,000 in
2014. It however recorded £192,000 as the median which was larger than the national mean for
England and wales.
Graph price against the years
1995 2000 2005 2010 2015
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
500000
f(x) = − 161.318868255145 x² + 659981.58024348 x − 674551234.400093
f(x) = 216.413472518692 x² − 847245.775620898 x + 828995755.071176
f(x) = 81.073461051685 x² − 309524.834507016 x + 294891894.463324f(x) = 81.073461051685 x² − 309524.834507016 x + 294891894.463324
f(x) = − 385.119670957648 x² + 1551697.4582635 x − 1562807726.99835
Chart Title
England and Wales
Polynomial (England and Wales)
London
Polynomial (London)
Polynomial (London)
Inner London
Polynomial (Inner London)
Outer London
Polynomial (Outer London)
Median house prices, pounds
Median house prices, pounds Compound growth rate, %
1996 2007 2009 2014 1996-
2007
2007-
2009
2009-
2014
England
and
Wales
57,000 176,000 169,000 192,000 11 -2 3
London 77,000 265,000 250,000 364,000 12 -3 8
Inner
London
87,000 313,000 323,000 462,000 12 2 7
Outer
London
74,000 249,000 235,000 315,000 12 -3 6
The figures represented in table 1 potrays a large variation across various parts of London. In
2014, the going market rate was high in central boroughs with a relative high price of £857,000
and £1,198,000 in Westminster and Kensington respectively as per the records provided by Land
Registry. In Barking and Dagenham, the mean price for purchasing a house was £215,000 in
2014. It however recorded £192,000 as the median which was larger than the national mean for
England and wales.
Graph price against the years
1995 2000 2005 2010 2015
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
500000
f(x) = − 161.318868255145 x² + 659981.58024348 x − 674551234.400093
f(x) = 216.413472518692 x² − 847245.775620898 x + 828995755.071176
f(x) = 81.073461051685 x² − 309524.834507016 x + 294891894.463324f(x) = 81.073461051685 x² − 309524.834507016 x + 294891894.463324
f(x) = − 385.119670957648 x² + 1551697.4582635 x − 1562807726.99835
Chart Title
England and Wales
Polynomial (England and Wales)
London
Polynomial (London)
Polynomial (London)
Inner London
Polynomial (Inner London)
Outer London
Polynomial (Outer London)
Median house prices, pounds
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Compound growth rate change, % for a period of 20014 – 2018 when investing £400,000
2014 2018 Compound growth
rate change, %
between 2014 -
2018
England and
Wales
192, 000 400,000 =
400 , 000−192,000
192, 000
= 1.2%
London 364,000 400,000 400 , 000−364 , 000
364 , 000
= 0.1%
Inner London 462,000 400,000 400 , 000−462 ,000
46 2 , 000
= -0.13%
Outer London 315, 000 400,000 400 , 000−315 , 000
315 ,000
= 0.27%
2014 2018 Compound growth
rate change, %
between 2014 -
2018
England and
Wales
192, 000 400,000 =
400 , 000−192,000
192, 000
= 1.2%
London 364,000 400,000 400 , 000−364 , 000
364 , 000
= 0.1%
Inner London 462,000 400,000 400 , 000−462 ,000
46 2 , 000
= -0.13%
Outer London 315, 000 400,000 400 , 000−315 , 000
315 ,000
= 0.27%
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Differential Equation for Loan Repayment
dP(t )
dt =r . P ( t ) −M
Where:
P(t) – present value of the principal of the loan,
r – interest rate for the compounding period
M - the payment that we would make during the same compounding period.
Pay attention to the units used. Ensure that the units are the same for all variables.
The units are a bit confusing since the interest rate is mostly calculated in a monthly basis though
not always but it can be given in annual terms. Complexity grows when we think of adjustable
rate loans where they are not constant that is, they fluctuate from time to time.
The equation is readjusted as follows
dP(t )
dt −r . P ( t ) =M
We then separate out the homogeneous form
dP(t)
dt −r . P ( t ) =0
Solution
Normally, we solve by finding a function which offers a solution to (3). After that we format it
so that it relates to the actual inhomogeneous solution. In technical subjects, we start with a "trial
solution". In other terms, we create a replica of the possible to the equation. In this instance, an
exponential function is the preferred choice.
P ( t ) =A . ekt +C
A and C are constants. They are used as adjustments to tune up the solution until it works. By
taking the derivative of this solution then substitute in (3), we obtain
k =r∧C=0 ………………………………….(5)
And are supposed to satisfy the equation. K is the interest rate. Substituting k =rinto (2) we find
−r . C=−M∨C= M
r ………………….(6)
It results to general solution which is true for all loans with fixed payments and interest rates.
Taking P(t=0) as the initial amount borrowed, we get
dP(t )
dt =r . P ( t ) −M
Where:
P(t) – present value of the principal of the loan,
r – interest rate for the compounding period
M - the payment that we would make during the same compounding period.
Pay attention to the units used. Ensure that the units are the same for all variables.
The units are a bit confusing since the interest rate is mostly calculated in a monthly basis though
not always but it can be given in annual terms. Complexity grows when we think of adjustable
rate loans where they are not constant that is, they fluctuate from time to time.
The equation is readjusted as follows
dP(t )
dt −r . P ( t ) =M
We then separate out the homogeneous form
dP(t)
dt −r . P ( t ) =0
Solution
Normally, we solve by finding a function which offers a solution to (3). After that we format it
so that it relates to the actual inhomogeneous solution. In technical subjects, we start with a "trial
solution". In other terms, we create a replica of the possible to the equation. In this instance, an
exponential function is the preferred choice.
P ( t ) =A . ekt +C
A and C are constants. They are used as adjustments to tune up the solution until it works. By
taking the derivative of this solution then substitute in (3), we obtain
k =r∧C=0 ………………………………….(5)
And are supposed to satisfy the equation. K is the interest rate. Substituting k =rinto (2) we find
−r . C=−M∨C= M
r ………………….(6)
It results to general solution which is true for all loans with fixed payments and interest rates.
Taking P(t=0) as the initial amount borrowed, we get

P0= A . er .0+ M
r
A=P0− M
r ………………………..(7)
Assuming that we know P0∧r , 2 variables are still unknown. If we know the life of the loan as
P ( t=T ) =0. Applying we obtain;
0=A . er .T + M
r
A=−M
r .e−r .T …………………(8)
Substituting (8) into (7);
P ( t ) = M
r ¿ ……………………………….(9)
Where M = P0 r
1−e−r .T
While the amount repaid = P(t) + M
In our case study
P0 = £400,000
T = 25 years = 25 * 12 = 300 months
Interest rate to be tested = 1%, 3%, 5%, 7%, 10% per month
Amount repaid = P(t) + M
P(t) per month = 400000/300 = 1333
Interest rate of 1%
M = P0 r
1−e−r .T
¿ £ 1333∗1 %
1−e−1 %∗300
= £14
r
A=P0− M
r ………………………..(7)
Assuming that we know P0∧r , 2 variables are still unknown. If we know the life of the loan as
P ( t=T ) =0. Applying we obtain;
0=A . er .T + M
r
A=−M
r .e−r .T …………………(8)
Substituting (8) into (7);
P ( t ) = M
r ¿ ……………………………….(9)
Where M = P0 r
1−e−r .T
While the amount repaid = P(t) + M
In our case study
P0 = £400,000
T = 25 years = 25 * 12 = 300 months
Interest rate to be tested = 1%, 3%, 5%, 7%, 10% per month
Amount repaid = P(t) + M
P(t) per month = 400000/300 = 1333
Interest rate of 1%
M = P0 r
1−e−r .T
¿ £ 1333∗1 %
1−e−1 %∗300
= £14
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Amount repaid per month=¿ 1333 + 14 = 1,347
Interest rate of 3%
M = P0 r
1−e−r .T
¿ £ 1333∗3 %
1−e−3 %∗300
= £40
Amount repaid per month=¿ 1333 + 40 = 1,373
Interest rate of 5% per month
M = P0 r
1−e−r .T
¿ £ 1333∗5 %
1−e−5 %∗300
= £67
Amoun t repaid per month=¿ 1333 + 67 = 1,400
Interest rate of 7%
M = P0 r
1−e−r .T
¿ £ 1333∗7 %
1−e−7 %∗300
= £93
Amount repaid per month=¿ 1333 + 93 = 1,426
Interest rate of 10%
M = P0 r
1−e−r .T
¿ £ 1333∗10 %
1−e−10%∗300
Interest rate of 3%
M = P0 r
1−e−r .T
¿ £ 1333∗3 %
1−e−3 %∗300
= £40
Amount repaid per month=¿ 1333 + 40 = 1,373
Interest rate of 5% per month
M = P0 r
1−e−r .T
¿ £ 1333∗5 %
1−e−5 %∗300
= £67
Amoun t repaid per month=¿ 1333 + 67 = 1,400
Interest rate of 7%
M = P0 r
1−e−r .T
¿ £ 1333∗7 %
1−e−7 %∗300
= £93
Amount repaid per month=¿ 1333 + 93 = 1,426
Interest rate of 10%
M = P0 r
1−e−r .T
¿ £ 1333∗10 %
1−e−10%∗300
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= 0
Amount repaid per month=¿ 1333 +0 = 1,333
Interest rate Amount repaid per
month for 25 years
period
1% 1347
3% 1373
5% 1400
7% 1426
10% 1333
0 2 4 6 8 10 12
1280
1300
1320
1340
1360
1380
1400
1420
1440
% Intrest rate
Amount repaid per month
Amount repaid per month=¿ 1333 +0 = 1,333
Interest rate Amount repaid per
month for 25 years
period
1% 1347
3% 1373
5% 1400
7% 1426
10% 1333
0 2 4 6 8 10 12
1280
1300
1320
1340
1360
1380
1400
1420
1440
% Intrest rate
Amount repaid per month

Alternative method
Using excel spreadsheet
Monthly payment will be determined by;
= PMT (rate, period, -Amount)
Loan
amount
1,333
Interest rate 1%
Period (in
months)
300
Compound
period per
year
12
Monthly
payment
$5.02
Amount
paid
1,338
Interest rate of 3%
Loan
amount
1,333
Using excel spreadsheet
Monthly payment will be determined by;
= PMT (rate, period, -Amount)
Loan
amount
1,333
Interest rate 1%
Period (in
months)
300
Compound
period per
year
12
Monthly
payment
$5.02
Amount
paid
1,338
Interest rate of 3%
Loan
amount
1,333
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