Gerritt wants to buy a car that costs 26750 The interest rat

Gerritt wants to buy a car that costs $26,750. The interest rate on his loan is 5.33 percent compounded monthly and the loan is for 7 years. What are his monthly payments? O $389.86 O $369.50 O $382.24 O $380.55 $40136

Solution

382.24 ,

Present value of ordinary annuity = Payment * [1 - (1+ interest)^{- number of payments}] / interest

26750 = Payment * [1 - (1+ 5.33%/12)^{- 7*12}] / (5.33%/12)

26750 = Payment * [1 - (1+ 0.004442)^{- 84}] / 0.004442

26750 = Payment * [1 - 1/(1.004442) ⁸⁴] / 0.004442

26750 = Payment * [1 - 1/1.451071] / 0.004442

26750 = Payment * 0.310854 / 0.004442

    26750 = Payment * 69.980639

26750 / 69.980639 = payment

$382.24 = payment