Question

Mary Smith took a car loan of $32,000 to pay back in 36 monthly installments at an interest rate of 8%. Compute the loan balance immediately after the 24th payment. Group of answer choices(a) the monthly payment for Mary.

(b) the loan balance immediately after the 24th payment.

(c) the monthly payment for the remainder of the loan if the interest rate is reduced to 9% compounded monthly.

Answer 1

Step-by-step explanation:

(a)the monthly payment for Mary

Given that the nominal interest rate = 8%

or, Monthly interest rate = 8%/12= 0.667%

Thus the monthly payment at 0.667% int. per month, A1 = $32,000 (A/P, 0.0067%, 36) =

loan ÷ [ (1-(1 / (1+r∧n))) / r ]

32,0000 ÷ [ (1-(1 / (1+0.00667∧60))) / 0.00667 ]

32,000 ÷ 49.3138 = $648.91

(b)the loan balance immediately after the 24th payment

After the 24th payment, 12 more payments will be left before the loan is retired.

648.91 × [ (1-(1 / (1+0.00667∧12))) / 0.00667 ]

= $7459.57

(c)the monthly payment for the remainder of the loan if the interest rate is reduced to 9%

Given that the nominal interest rate is 9%,

or, Monthly interest rate = 9%/12 = 0.75%

Thus the monthly payment at 3/4% int. per month, A2 = $7459.57 (A/P, 0.75%, 12) =

7459.57 ÷ [ (1-(1 / (1+0.0075∧12))) / 0.0075 ]

7459.57 ÷ 11.4349

= $652.35