College

Kendra took out a loan for [tex]\$750[/tex] at an [tex]8.4\%[/tex] APR, compounded monthly, to buy a stereo. If she will make monthly payments of [tex]\$46.50[/tex] to pay off the loan, which of these groups of values plugged into the TVM Solver of a graphing calculator could be used to calculate the number of payments she will have to make?

A. [tex]N=; I\%=8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;[/tex] PMT: END

B. [tex]N=; I\%=0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;[/tex] PMT: END

C. [tex]N=; I\%=8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12;[/tex] PMT: END

D. [tex]N=; I\%=0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12;[/tex] PMT: END

Answer :

To solve the problem of determining the appropriate values for the TVM (Time Value of Money) Solver in a graphing calculator, follow these steps:

1. Understand the Loan Details:
- Principal amount ([tex]\(PV\)[/tex]): [tex]\(-\$750\)[/tex] (negative because it's a loan taken out)
- Monthly payment ([tex]\(PMT\)[/tex]): [tex]\(\$46.50\)[/tex]
- Loan is to be paid off entirely, so Future Value ([tex]\(FV\)[/tex]): [tex]\(0\)[/tex]
- Annual Percentage Rate (APR): [tex]\(8.4\%\)[/tex]
- Compounded monthly

2. Calculate Monthly Interest Rate:
- Since the APR is [tex]\(8.4\%\)[/tex] and it's compounded monthly, you need to convert this annual rate into a monthly rate.
- Monthly interest rate = [tex]\( \frac{8.4\%}{12} = 0.7\%\)[/tex]

3. Components in TVM Solver:
- [tex]\(N\)[/tex]: This is what we need to determine—the number of payments.
- [tex]\(i\%\)[/tex]: Interest rate per period, which is [tex]\(0.7\%\)[/tex] monthly (as calculated).
- [tex]\(PV\)[/tex]: Present value or principal = [tex]\(-750\)[/tex]
- [tex]\(PMT\)[/tex]: Monthly payment = [tex]\(46.5\)[/tex]
- [tex]\(FV\)[/tex]: Future value = [tex]\(0\)[/tex]
- [tex]\(P/Y\)[/tex]: Payments per year = 12 (monthly payments)
- [tex]\(C/Y\)[/tex]: Compounding periods per year = 12 (monthly compounding)
- Payments at the end of the period (PMT:END)

4. Identify the Correct Option:
- Option A uses an interest rate of [tex]\(8.4\%\)[/tex] and monthly compounding but incorrectly sets [tex]\(P/Y\)[/tex] to 1.
- Option B correctly uses [tex]\(i\% = 0.7\%\)[/tex] but incorrect [tex]\(P/Y = 1\)[/tex].
- Option C uses [tex]\(i\% = 8.4\%\)[/tex] with correct [tex]\(P/Y\)[/tex] and [tex]\(C/Y\)[/tex] of 12.
- Option D correctly uses [tex]\(i\% = 0.7\%\)[/tex], [tex]\(P/Y = 12\)[/tex], and [tex]\(C/Y = 12\)[/tex].

Therefore, the correct choice is Option D. This option uses the correct monthly interest rate and aligns the number of payments with monthly compounding and payments.