Question

It is time to buy a used Toyota Camry. You got a loan for 10 years. The car cost you $12,000. It is not a new car but in very decent shape. The bank expects you to pay $150 a month. Calculate the EAR.

Please provide a written answer. Thank you

Answer 1

The question is solved by calculating the yield to maturity of the loan

Time= 10 years*12= 120 months

Present value= $12,000

Monthly payment= $150

The yield to maturity is calculated by entering the below:

‘PV= -12,000; N= 120; PMT= 150

Press CPT and I/Y to calculate the yield to maturity.

The yield to maturity is 0.7241 per month and 0.7241*12= 8.6892 per year.

The 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+0.0869/12)^12-1

        = 1.0904-1

        = 0.0904*100= 9.04%

Therefore, the effective annual rate is 9.04%.