Exploration in Mathematics: Calculations for Buying a House and Car

This article provides step-by-step mathematical calculations for buying a house and car. It includes calculations for EMI, interest payments, and money saved by refinancing. The article is useful for students studying mathematics and finance. The calculations are done for a house priced at $350,000 and a car priced at $30,750.

EXPLORATION IN MATHEMATICS
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The link to the property is indicated below.
https://denver.coloradohomefinder.com/homes/7695-Barbara-Ann-Drive/Arvada/CO/
80004/82134926/
Question 1
The asking price for the house is $350,000.
Question 2
Downpayment = (20/100)*350000 = $ 70,000
Hence, financing required to buy the house = 350000 – 70000 = $ 280,000
Question 3
The formula for EMI (Equal monthly instalment) is indicated below.
EMI = [P x R x (1+R)N]/[(1+R)N-1]
For the given case, P= $280,000, N= 30 years or (30*12 = 360 months), R= 4.25% p.a. or
(4.25/12 = 0.354% per month)
Hence, EMI = 280000*(0.00354)*(1.00354)360/[(1.00354)360-1] = $1,377.43
Question 4
Interest amount on first payment= (0.354/100)*280000 = $ 991.67
Question 5
The amount owed on the house after 10 years would amount to $214,342.2. This has been
obtained by deducting the total principal repayments from the original principal amount of
$280,000.
Question 6
Total payment for the 30 year loan = 1377.43*360 = $495, 875.4

Question 7
Interest payment on the loan = Total payment – Principal amount = 495, 875.4 - 280,000 = $c
Question 8
The formula for EMI (Equal monthly instalment) is indicated below.
EMI = [P x R x (1+R)N]/[(1+R)N-1]
For the given case, P= $280,000, N= 15 years or (15*12 = 180 months), R= 4% p.a. or (4./12
= 0.333% per month)
Hence, EMI = 280000*(0.00333)*(1.00333)180/[(1.00333)180-1] = $2,071.13
Question 9
Interest amount on first payment= (0.333/100)*280000 = $ 933.33
Question 10
Total payment for the 15 year loan = 2071.13*180 = $372,802.7
Question 11
Interest payment on the loan = Total payment – Principal amount = 372,802.7 - 280,000 =
$92,802.7
Question 12
Money saved by refinancing = Difference in the interest payments = $215,875.4 - $92,802.7
= $123,072.7
The link for the automobile is as follows.
https://www.cargurus.com/Cars/l-Used-BMW-m3#listing=198034044
Question 13

The asking price for the automobile is $30,750.
Question 14
Trade in amount = $6,500
Amount to be financed = 30750 – 6500 = $24,250
Question 15
The formula for EMI (Equal monthly instalment) is indicated below.
EMI = [P x R x (1+R)N]/[(1+R)N-1]
For the given case, P= $24,250, N= 5 years or (5*12 = 60 months), R= 3.25% p.a. or (3.25/12
= 0.271% per month)
Hence, EMI = 24250*(0.00271)*(1.00271)60/[(1.00271)60-1] = $ 438.44
Question 16
Total payment for the 5 year loan = 438.44*60 = $26,306.4
Question 17
Interest payment on the loan = Total payment – Principal amount = 26,306.4 – 24,250 =
$2,056.4