Consumer Mathematics: Analyzing Loans, Mortgages, and Investments

This document provides a comprehensive solution to a consumer mathematics assignment. It explores practical financial problems, including loan repayment, mortgage calculations, and investment strategies. The assignment begins by calculating the total installment cost and interest paid on a loan using the compound interest formula. It then determines the annuity payment required to reach a specific savings target over a set period. Finally, it calculates the monthly mortgage payment, considering the principal amount, interest rate, and loan duration. The solutions demonstrate how mathematical principles can be applied to manage personal finances effectively and avoid potential financial penalties. The assignment also includes a reference to a relevant textbook.

Consumer mathematics
Introduction
This exercise will demonstrate the use of mathematical principles to handle practical business
and finance problems such as loan repayment, mortgage and payments and general future
planning
Question 1: Compound Interest
Solution
Principal amount, P = $4800
Interest rate, r = 10% per annum
The rate of interest per month is: r = 10/(1200) = 0.008333
Duration of repayment = n = 3 years
Total number of months = n×12 = 3 × 12 = 36
Since the loan is paid per month, we can consider this as EMI
From the relationship;
EMI = P×r (1 + r)n / ((1 + r)n – 1)
EMI = 4800 × 0.008333 (1 + 0.008333)36/ ((1 + 0.008333)36 -1)
= $154.88
Therefore, his total installment cost, C = 154.88 × 36 = 5575.68 $
Total interest = C – P = 5575.68 – 4800 = $775.68
Question 2: Annuity Payment
Solution
Let monthly deposit be denoted by D
r is the rate of interest per year = 7%
Therefore, interest rate per month = 0.07
12 0.005833

n is the total number of months = 2 × 12 = 24 months
Target savings, T = 15000 $
T = D [(1+r ) n – 1]/¿
r ¿
15000 = D[(1 + 0.005833)24 -1] ÷ 0.005833
From which the annuity payment, D = $584.09
Question 3: Mortgage Financing
Solution
The total payment per month is given by the following formula:
M = P∗[r ( 1+r ) n]
((1+r )n−1)
Where P denotes the initial amount paid (principal amount)
r denotes interest rate.
n denotes the duration in months
P = 129,000 – 10,000 = 119,000
the interest rate per month = 6%/12 = 0.50%
n = 30 * 12 = 360 months
So, M = 119,000 * [0.0050 (1.0050)360/(1.0050360 – 1)]
M = 119,000 * 0050 * 6.0225 / 5.0225
M = $713.47
Therefore, the total payment per month = M + PMI
= 713.47 + 25
= $738.47
Conclusion.
From the above calculations, it is evident that this branch of mathematics is an invaluable tool
for proper planning of one’s finances. This helps avoid capital mismanagement which can result
in penalties.

Reference
Blitzer, R. (2015). Thinking Mathematically (6th ed.). Boston MA: Pearson Education