Question

You take out a $9,000 car loan that calls for 36 monthly payments starting after 1 month at an APR of 9%.
a. What is your monthly payment? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
b. What is the effective annual interest rate on the loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
c. Now assume the payments are made in four annual year-end installments. What annual payment would have the same present value as the monthly payment you calculated? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a. Information provided:

Present value= $9,000

Time= 36 months

Interest rate= 9%/12= 0.75% per month

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

PV= -9,000

N= 36

I/Y= 0.75

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

The value obtained is 286.20.

Therefore, the monthly payment is $286.20.

b.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+0.09/12)^12 – 1

        = 1.0938 – 1

        = 0.0938*100

        = 9.38%.

c. The annual payment iscalculated by entering the below in a financial calculator:

PV= -9,000

N= 4

I/Y= 9

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

The value obtained is 2,778.02.

Therefore, the annual payment is $2,778.02.