Consumer mathematics.

Option #1: Consumer Mathematics #1 Compound Interest Bob bought hunting equipment for $4,800. He borrowed money from his credit union for the purchase, obtaining a loan with a 10% annual interest rate, monthly compounding, and a 3-year term. If Bob’s loan is structured as an installment loan, calculate his total installment cost, his monthly payment, and his total finance charge (interest). Annuity Payment David is saving money to open an Indian food franchise. He needs $15,000 in two years to make his down payment and is investing in an annuity yielding an annual interest rate of 7% compounded monthly. If the annuity requires that David make monthly investments, what annuity payment must David make to save $15,000? Mortgage Financing Abbie purchased a $129,000 home with 30-year term, 6% rate mortgage. At closing she paid a $10,000 down payment, requiring her to purchase private mortgage insurance (PMI) at a cost of $25 per month. Calculate Samantha’s monthly mortgage plus PMI payme

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