Question

Penny's parents have agreed to loan her $4500 to pay her tuition. They are charging her an interest rate of

3% per annum, compounded monthly. Penny has arranged to pay them $160 per month to pay off the loan.
a) how long it takes Penny to pay off the loan b) the amount of her final payment

Answer 1

$157.92.

Explanation:

a) To calculate how long it takes Penny to pay off the loan, we can use the formula:

n = log(P/A) / log(1 + r/12),

where n is the number of months, P is the initial loan amount ($4500), A is the monthly payment ($160), and r is the annual interest rate (3%).

n = log(4500/160) / log(1 + 0.03/12)

n = log(28.125) / log(1.0025)

n = 3.7062

Rounding up, it takes Penny 4 months to pay off the loan.

b) To calculate the amount of Penny's final payment, we can use the formula:

P = A * (1 - (1 + r/12)^-n),

where P is the remaining balance, A is the monthly payment ($160), n is the number of months (4), and r is the annual interest rate (3%).

P = 160 * (1 - (1 + 0.03/12)^-4)

P = 160 * (1 - (1.0025)^-4)

P = $157.92

Therefore, it takes Penny 4 months to pay off the loan and her final payment is $157.92.