High School

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 = 12 ; 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 = 1 ; C/Y = 12[/tex]; PMT: END

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

Answer :

We start by recalling that Kendra’s APR is [tex]\(8.4\%\)[/tex] and the interest is compounded monthly. This means the monthly interest rate is calculated by dividing the APR by the number of months in a year. That is,

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

When setting up the TVM (Time Value of Money) calculation on a graphing calculator, we need to enter the following values:

1. [tex]\(PV = -750\)[/tex] (The loan amount is entered as a negative number because it represents an outflow.)
2. [tex]\(PMT = 46.50\)[/tex] (The monthly payment is positive as it represents money coming in to pay off the loan.)
3. [tex]\(FV = 0\)[/tex] (This indicates that the loan is fully paid off at the end.)
4. The monthly interest rate is [tex]\(0.7\%\)[/tex] (not [tex]\(8.4\%\)[/tex]. This is crucial since the calculator requires the rate per compounding period.)
5. [tex]\(P/Y = 12\)[/tex] and [tex]\(C/Y = 12\)[/tex] to reflect the monthly payments and monthly compounding.

Reviewing the multiple-choice options, we see that Option B uses values:

- Interest rate: [tex]\(0.7\%\)[/tex]
- [tex]\(PV = -750\)[/tex]
- [tex]\(PMT = 46.50\)[/tex]
- [tex]\(FV = 0\)[/tex]
- [tex]\(P/Y = 12\)[/tex]
- [tex]\(C/Y = 12\)[/tex]

This matches exactly with our requirements.

Therefore, the correct group of values to plug into the TVM solver is:

Option B.