Question

Karen borrowed money from her credit union to invest in antiques. She took out a personal, amortized loan for $27,000, at an interest rate of 7.75%, with monthly payments for a term of 3 years. Round your answer to each of the following questions to the nearest cent.

(a) Find Karen’s montly payment.

Answer 1

To determine Karen's monthly payment for the $27,000 loan at 7.75% interest over 3 years, we use the loan amortization formula, yielding a payment of approximately $844.90.

Step-by-step explanation:

To calculate Karen's monthly payment for her personal amortized loan, we use the loan amortization formula which considers the principal amount, the monthly interest rate, and the number of payments:

To find the monthly payment for Karen's loan, we can use the formula for the monthly payment of an amortized loan

Monthly Payment = P * (r(1+r)^n) / ((1+r)^n - 1)

Where:
P = Principal amount ($27,000)
r = Monthly interest rate (7.75%/12 months = 0.00645833)
n = Total number of payments (3 years * 12 months = 36)

Substituting the values:

Monthly Payment = $27,000 * (0.00645833(1+0.00645833)^36) / ((1+0.00645833)^36 - 1)

Monthly Payment ≈ $844.90

Therefore, Karen's monthly payment for the loan is approximately $844.90.