Question

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

a) $6383.60
b) $1,152,128

c) Keisha will pay a total of $1,100,128 in interest over the course of the loan.

Explanation:

(a) To find Keisha's monthly payment, we can use the following formula:

monthly payment = loan amount * (monthly interest rate / (1 - (1 + monthly interest rate)^(-number of payments)))

Substituting in the given values, we get:

monthly payment = 52000 * (0.051 / (1 - (1 + 0.051)^(-180)))

= 52000 * (0.051 / (1 - (1.051)^(-180)))

= 52000 * (0.051 / (1 - 0.586))

= 52000 * (0.051 / 0.414)

= 52000 * 0.123

= $6383.60

(b) To find the total amount Keisha will pay to repay the loan, we can multiply the monthly payment by the number of payments:

total amount = monthly payment * number of payments

= 6383.60 * 180

= $1,152,128

(c) To find the total amount of interest Keisha will pay, we can subtract the loan amount from the total amount:

total interest = total amount - loan amount

= 1152128 - 52000

= $1,100,128

So Keisha will pay a total of $1,100,128 in interest over the course of the loan.