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

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

C. [tex]N = ; I\% = 0.7 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 1 ; 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 a TVM (Time Value of Money) Solver on a graphing calculator to calculate the number of payments Kendra will have to make, let’s break down the information given and apply it to each option:

Loan Details:
- Loan amount (Present Value, PV): [tex]$750 (treated as negative since it's money owed)
- Annual Percentage Rate (APR): 8.4%
- Monthly payments (PMT): $[/tex]46.50
- Future Value (FV): 0 (since the loan will be fully paid off)
- Payments per year (P/Y): 12 (monthly payments)
- Compounding periods per year (C/Y): 12 (monthly compounding)

Now, let's review each option:

- Option A:
- Interest rate ([tex]\(I\%\)[/tex]): 0.7%
- PV: -750
- PMT: 46.5
- FV: 0
- P/Y: 12
- C/Y: 12

The interest rate is incorrect here. It should be the annual rate of 8.4%.

- Option B:
- Interest rate ([tex]\(I\%\)[/tex]): 8.4%
- PV: -750
- PMT: 46.5
- FV: 0
- P/Y: 12
- C/Y: 12

Everything matches perfectly here. The interest rate is correct, as well as the number of payments and compounding periods per year.

- Option C:
- Interest rate ([tex]\(I\%\)[/tex]): 0.7%
- PV: -750
- PMT: 46.5
- FV: 0
- P/Y: 1
- C/Y: 12

Although the P/Y value is incorrect (it should be 12), the interest rate is also wrong.

- Option D:
- Interest rate ([tex]\(I\%\)[/tex]): 8.4%
- PV: -750
- PMT: 46.5
- FV: 0
- P/Y: 1
- C/Y: 12

While the interest rate is correct, the P/Y (payments per year) is incorrectly set to 1.

Conclusion:
The correct group of values that match all the loan terms is Option B. This option uses the appropriate 8.4% annual interest rate and correctly sets both 12 payments per year and 12 compounding periods per year. Therefore, the correct choice is B.