College

Kendra took out a loan for [tex]$\$[/tex]750[tex]$ at an $[/tex]8.4\%[tex]$ APR, compounded monthly, to buy a stereo. If she will make monthly payments of $[/tex]\[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]$N=; I\%=0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;$[/tex] PMT:END

B. [tex]$N=; I\%=0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12;$[/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]$N=; I\%=8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;$[/tex] PMT:END

Answer :

To determine which group of values could be used in the Time Value of Money (TVM) Solver on a graphing calculator, let's focus on understanding each part of the problem:

### Key Information:
- Loan Amount (PV): [tex]$750 (since the loan is taken out, this is a negative value in the calculator)
- Annual Percentage Rate (APR): 8.4%
- Monthly Payment (PMT): $[/tex]46.50
- Future Value (FV): $0 (she wants to pay off the loan completely)
- Payments per Year (P/Y): Since she makes monthly payments, this is 12.
- Compounding per Year (C/Y): Since the interest is compounded monthly, this is also 12.

### Understanding the Interest Rate:
1. Annual Rate (APR): 8.4%
2. Monthly Interest Rate: Divide the annual rate by 12 (since there are 12 months in a year).

[tex]\[
\text{Monthly Interest Rate (\%)} = \frac{8.4\%}{12} \approx 0.7\%
\][/tex]

### Matching the Values with the Options:
With these inputs, we need to set up the TVM Solver with:

- [tex]\(N\)[/tex]: The number of payments to be determined.
- [tex]\(I\%\)[/tex]: The monthly interest rate we calculated, 0.7%.
- [tex]\(PV\)[/tex]: -750 (the present value is inputted as a negative as it’s money owed).
- [tex]\(PMT\)[/tex]: 46.50
- [tex]\(FV\)[/tex]: 0
- [tex]\(P/Y\)[/tex]: 12 (since payments are monthly)
- [tex]\(C/Y\)[/tex]: 12 (since compounding is also monthly)

Now let's check through, option by option:

- Option A has [tex]\(P/Y = 1\)[/tex] which is incorrect because payments are indeed monthly, so [tex]\(P/Y\)[/tex] should be 12.
- Option B and Option C both feature [tex]\(P/Y = 12\)[/tex] and [tex]\(C/Y = 12\)[/tex], but only Option B has the correct [tex]\(I\%\)[/tex] input of 0.7%.

### Conclusion:
The correct setup, where the monthly interest rate is 0.7%, payments per year are 12, and compounding per year is also 12, aligns with Option B:

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

So the correct choice is Option B.