Question

Evan had to make payments of $1,125 every 6 months to settle a $27,000 loan that he

received at 5.12% compounded semi-annually. How long did it take to settle the loan?
years
months
Express the answer in years and months, rounded up to the next month

Answer 1

We can use the formula for the present value of an annuity to solve this problem:

PV = PMT x ((1 - (1 + r/n)^(-nt)) / (r/n))

where PV is the present value of the loan, PMT is the payment, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the given values, we get:

27000 = 1125 x ((1 - (1 + 0.0512/2)^(-2t)) / (0.0512/2))

Simplifying and solving for t, we get:

t = (1/2) x log(1 + (27000 x 0.0512/2) / 1125) / log(1 + 0.0512/2)

t ≈ 4.5 years

So it took Evan about 4 years and 6 months (rounded up to the next month) to settle the loan.