Question

To help pay for art school, Keisha borrowed money from an online lending company.

She took out a personal, amortized loan for $52,000, at an interest rate of 5.1%, with monthly payments for a term of 15 years.

(a)Find Keisha's monthly payment.

(b) If Keisha pays the monthly payment each month for the full term, find her total amount to repay the loan.

(c) If Keisha pays the monthly payment each month for the full term, find the total amount of interest she will pay.

Answer 1

• payment: $413.93
• total repaid: $74,507.40
• interest: $22,507.40

Explanation:

(a) The monthly payment A on principal P at monthly rate r for n months can be computed using ...

A = Pr/(1 -(1+r)^-n)

For P=$52000, r = .051/12 = 0.00425, n = 12*15 = 180, the payment is ...

A = $52000·0.00425/(1 -1.00425^-180) ≈ $413.93

(b) The total of 180 payments is ...

180 · $413.93 = $74,507.40

(c) The difference from the principal is the interest paid:

$74,507.40 -52,000 = $22,507.40