Question

Danny recently borrowed $30,000 from the Eicher Credit Union with the loan repayments specified at $1,000 payable at the end of each month for the next 3 years. He has annual earnings of $75,000 which are likely to remain constant over the next 3 years. Calculate Danny’s purchasing power for each of the next 3 years.

Answer 1

EMI = [P x R x (1+R)^N] / [(1+R)^N - 1],

where P stands for the loan amount or principal,

R is the interest rate per month [if the interest rate per annum is 12%, then the monthly rate of interest will be 1%]

and N is the number of monthly installments

Here, N = 3*12 = 36 months

P = loan principal = $30,000

EMI = $1,000

Substituting the values in the formula above, we get the annual interest rate, R = 12.25%

Borrowed amount ($)	30000
Interest rate	12.25%
Time period (years)	3
PMT ($)	1000

Annual earnings = $75,000

Monthly earnings = $75000/12 = $6,250

Monthly loan expenses = $1,000

Monthly savings = $5,250

It's a monthly annuity. The present value of an annuity is given by:

P = Monthly savings = $5,250

r = Interest rate per period = 12.25%/12 = 1.02%

n = no. of periods = 36 months

Purchasing power, PV (monthly savings) = $187,500