Prescott Bank offers you a five-year loan for $55,000 at an annual interest rate of 7.25 percent. What will your annual loan payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

Annual loan payment = $13,146.78

Explanation:

Loan Amortization: A loan repayment method structured such that a series of equal periodic installments will be paid for certain number of periods to offset both the loan principal amount and the accrued interest.

The monthly equal installment is calculated as follows:  

Monthly equal installment= Loan amount/Monthly annuity factor  

Monthly annuity factor  

=( 1-(1+r)^(-n))/r  

r- Monthly interest rate (r)  

= 7.25%/12= 0.604 %  

n- Number of months ( n) in 5 years  

= 12* 6 = 60  

Annuity factor  

= ( 1- (1.00604)^(-60)/0.00604= 50.2024

Monthly installment= 55,000 /50.2024 = $1,095.56

 Monthly installment = $1,095.56

Annual loan payment = monthly installment × 12

Annual loan payment =$1,095.56 ×12=13,146.78

Annual loan payment = $13,146.78

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