A loan of $15 000.00 was repaid together with interest of $1089.00. If interest was 5% compounded quarterly, how long was the loan taken out? (Answers are rounded off to years and months)

Question

Quizplus · Accepted Answer

To solve the problem, we can use the formula:

A = P(1 + r/n)^(nt)

Where:
A = the total amount repaid (principal + interest)
P = the principal (loan amount)
r = the interest rate per year (as a decimal)
n = the number of times the interest is compounded per year
t = the time duration of the loan (in years)

We can rearrange the formula to solve for t:

t = (1/n) * log(A/P) / log(1 + r/n)

With the given values, we have:

P = $15 000.00
A = $15 000.00 + $1089.00 = $16 089.00
r = 5% = 0.05
n = 4 (compounded quarterly)

Plugging these values into the formula, we get:

t = (1/4) * log(16089/15000) / log(1 + 0.05/4) ≈ 1.4 years

So the answer is C) 1 year 5 months.

A Loan of $15 000