Question

In: Finance

You have just seen an ad for season tickets to the 2020 and 2021 Chiefs games....

You have just seen an ad for season tickets to the 2020 and 2021 Chiefs games. The ad says these double-season tickets can be purchased today for $5,000. Alternatively, they can be purchased on the installment plan, for a monthly payment of $250, to be paid at the beginning of each month for 24 months (the first payment is due on the day you buy the tickets). What is the Effective Annual Rate (EAR) on the installment purchase?

Expert Solution

Information provided:

Present value= $5,000

Time= 24 months

Monthly payment = $250

The question is concerning finding the interest rate of an annuity due. 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.

The monthly interest rate is calculated by entering the below in a financial calculator in BGN mode:

PV= -5,000

N= 24

PMT= 250

Press the CPT key and I/Y to compute the monthly interest rate.

The value obtained is 1.6550

Therefore, the amount of annual interest rate is 1.6550*12 = 19.86%.

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+0.1986/12)^12 - 1

= 1.2177 - 1

= 0.2177*100

= 21.77%.

Therefore, the effective annual rate is 21.77%.

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

jeff jeffy answered 1 year ago

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