Question

Martha ross took out a loan to pay for her child's education for $50,000. the loan would be repaid at the end of 9 years in one payment with an interest of 12 percent. the total amount martha has to pay back at the end of the loan is:

Answer 1

Given:
P = $50,000, the principal
r = 12% = 0.12, the interest rate
t = 9 years.

We are not given the compounding interval.
We shall consider two cases
(a) n = 12, monthly compounding
(b) n = 1, yearly compounding.

The value of the loan is given by
$A = P(1 + \frac{r}{n} )^{nt}$

When n=12, obtain
A = 50000( 1 +0.12/12)¹⁰⁸ = $146,446.29
When n=1, obtain
A = 50000(1 +0.12)⁹ = $138,653.94

Answer:
$146,446.29 for monthly compounding.
$138,653.94 for yearly compounding.