Question

You want to buy a car, and a local bank will lend you $30,000. The loan will be fully amortized over 3 years (60 months), and the nominal interest rate will be 5.25% with interest paid monthly. What will be the monthly loan payment?  What will be the loan’s EAR?

Answer 1

Information provided:

Present value= $30,000

Time= 60 months

Interest rate= 5.25%/12= 0.4375%

The monthly payment is calculated by entering the below in a financial calculator:

FV= -30,000

N= 60

I/Y= 0.4375

Press the CPT key and PMT to compute the monthly payment.

The value obtained is 569.58.

Therefore, the monthly payment is $569.58.

Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1+0.0525/12)^12-1

        = 1.0538-1

        = 0.0538*100= 5.38%

Therefore, the effective annual rate is 5.38%.

In case of any query, kindly comment on the solution.