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\%=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=12; 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 :

To find out how many payments Kendra will need to make, we need to use the TVM (Time Value of Money) Solver on a graphing calculator. Let's examine the values that need to be entered based on the options provided.

First, let's understand what each variable stands for in the TVM Solver:

- N: The number of payments to be made.
- I%: The annual interest rate as a percentage.
- PV: The present value or the initial amount of the loan (entered as a negative number because it represents an outflow).
- PMT: The payment per period (monthly payment in this case).
- FV: The future value of the loan, which will be zero because the loan will be paid off by the end of the term.
- P/Y: Payments per year.
- C/Y: Compounding periods per year.
- PMT:END: This means payments are made at the end of each period.

Given that Kendra's loan has an 8.4% APR compounded monthly, let's analyze which option is correct:

### Option Analysis:

1. Option A:
- I% = 8.4: Correct for annual interest rate.
- P/Y = 1 and C/Y = 12: The number of payments per year does not match monthly compounding, as P/Y should be 12.
- Therefore, Option A is incorrect.

2. Option B:
- I% = 8.4: Correct for the annual interest rate.
- P/Y = 12 and C/Y = 12: Both are correctly set for monthly payments and monthly compounding.
- Therefore, Option B correctly captures the scenario.

3. Option C:
- I% = 0.7: This suggests a monthly interest rate, which contradicts the given APR format of annual rate.
- P/Y = 12 and C/Y = 12: Correct for monthly payments and compounding.
- Using a monthly interest rate format here does not match the question's context, so it's not suitable for finding the number of payments accurately.

4. Option D:
- I% = 0.7: Like Option C, this implies a monthly interest rate.
- P/Y = 1 and C/Y = 12: Incorrect settings for monthly payments and compounding.
- Therefore, Option D is incorrect.

The correct set of values that correspond to Kendra's scenario and will yield the calculated number of payments she must make is found in Option B.