Question

A commercial bank will loan you $47,497 for 8 years to buy a car. The loan must be repaid in equal monthly payments at the end of the month. The annual interest rate on the loan is 10.16 percent of the unpaid balance. What is the amount of the monthly payments?

Answer 1

Answer: The monthly payments amount is equal to $724.75

Given that;
Present value of the loan is $47497, time period to repay the loan is 8 years in equal monthly payments and annual interest rate is 10.16%.

As the payments are made monthly, the monthly interest rate is 10.16%/12=0.008466667
The number of period when the payments are made monthly will be equal to 8*12=96
The formula to determine the monthly payments = (Rate of interest)*(Present value)/[1-(1+Rate of interest)^(-Number of periods)]
Monthly payments=(0.008466667)*(47497)/[1-(1+0.008466667)^(-96)]
=(402.1412825)/[1-(1.008466667)^(-96)]
=(402.1412825)/(1-0.445134641)
=(402.1412825)/0.554865359
Monthly payments=724.7547103 or $724.75 (Rounded to two decimal places)

Alternative solution using excel.
We can also solve the problem using excel as:
Present value=$47497
Monthly interest rate=0.008466667
Number of periods=96
As the loan will be paid off completely, the future value will be zero.
So, future value=$0

1 Present value 47497 2 Future value 3 Interest rate 0.008466667 4 Number of periods 5 Payments ($724.75) 6 Formula used: PMT(F3, F4,F1,F2) 96

So, monthly payments=$724.75
As payments are cash outflow, it is shown as negative in excel.

Please let me know if you find any difficulty in understanding the solution. Please give us feedback by rating the answer.