To determine (a) The monthly payments for the loan repayment period as 25 years. (b) The monthly payments if the loan needs to be repaid in 15 years. (c) The total amounts paid in both cases. Explanation Given: Starting loan principal = P = $60,000.00 Annual percentage rate = APR = 8% Number of payment periods per year = n = 12 Loan term in years = Y =25 years Prepayment term in years = 15 years. Formula used: P M T = P × ( A P R n ) [ 1 − ( 1 + A P R n ) − n Y ] Calculation: (a) To calculate the amount to be paid per month to complete the loan in 25 years, substitute the given values in the formula as shown. P M T = P × ( A P R n ) [ 1 − ( 1 + A P R n ) − n Y ] = ( $ 60 , 000 ) × ( 0.08 12 ) [ 1 − ( 1 + 0.08 12 ) − ( 12 × 25 ) ] Calculate the value of the numerator as ( $ 60 , 000 ) × ( 0.08 12 ) = $ 400 . Calculate the value of the denominator as follows. [ 1 − ( 1 + 0.08 12 ) − ( 12 × 25 ) ] = [ 1 − ( 1.0067 ) − 300 ] = 0.8651 Calculate the value of the monthly payments. P M T = $ 400 0.8651 = $ 462.37 (b) Keeping the APR rate constant, calculate the amount to be repaid if the loan term is to be repaid in 15 years. Keeping all other values, the same, substitute 15 years for Y in the expression. P M T = P × ( A P R n ) [ 1 − ( 1 + A P R n ) − n Y ] = ( $ 60 , 000 ) × ( 0...

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Author: Bennett

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Chapter 4.D, Problem 46E

To determine

(a) The monthly payments for the loan repayment period as 25 years.

(b) The monthly payments if the loan needs to be repaid in 15 years.

(c) The total amounts paid in both cases.

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Chapter 4.D, Problem 45E

Chapter 4.D, Problem 47E

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