Question

You want to purchase a new sports car from BD Motors for $70,000. The contract is in the form of a 48-month annuity-due at 8% interest APR. If you put $5,000 down today, what will the monthly payment be? What is the Effective Annual Rate (EAR)?

Answer 1

Information provided:

Cost of the car = $70,000

Down payment = $5,000

Present value (PV)= $70,000 - $5,000 = $65,000

Time (N)= 48 months

Monthly interest rate (I/Y)= 8%/12 = 0.6667%

Annuity due refers to annuity that occurs at the beginning of a period.

This can also be solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2^ndBGN 2^ndSET on the Texas BA II Plus calculator.

Enter the below in a financial calculator in BGN mode to compute the monthly payment of annuity due:

PV= 65,000

N= 48

I/Y= 0.6667

Press the CPT key and PMT to compute the monthly payment of annuity due.

The value obtained is 1,576.33.

Thereby, the monthly payment of annuity due is $1,576.33.

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+0.08/12)^12 - 1

= 1.0830 - 1

= 0.0830*100

= 8.30%.