College

Kendra took out a loan for [tex]\$750[/tex] at an 8.4% 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=1; \ C/Y=12;[/tex] PMT:END

B. [tex]N=; \ I\%=8.4; \ 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 correct group of values to input into the Time Value of Money (TVM) Solver on a graphing calculator, we need to analyze the details of Kendra's loan:

1. Loan Amount: [tex]$750
2. APR (Annual Percentage Rate): 8.4%
3. Compounding Frequency: Monthly
4. Monthly Payment: $[/tex]46.50

The goal is to find out how many payments Kendra needs to make to pay off this loan. Let's break down the elements typically required for the TVM Solver on a graphing calculator:

- N: Number of payments (what we are solving for)
- I%: Annual interest rate
- PV (Present Value): The initial loan amount, which is [tex]$750 (entered as -750 because it's an outgoing payment)
- PMT (Payment): Monthly payment which is $[/tex]46.50
- FV (Future Value): $0 (since we want the loan fully paid off)
- P/Y (Payments per Year): Number of payments made per year
- C/Y (Compounding per Year): Number of times interest is compounded per year

Given Kendra's loan information:

- P/Y = 12: Since payments are made monthly.
- C/Y = 12: Since the interest is compounded monthly.

Let's evaluate each choice:

A. Incorrect:
- I% = 0.7: This implies monthly interest is used directly, but the P/Y is set to 1, suggesting yearly payment which is inconsistent with monthly compounding and payments.

B. Incorrect:
- I% = 8.4: Correct use of the annual rate but P/Y is 1, which shows payments are made yearly instead of monthly.

C. Correct:
- I% = 8.4: Using the annual interest rate accurately.
- P/Y = 12: Payments are made monthly (12 times a year).
- C/Y = 12: Interest compounded monthly.
- This combination correctly aligns with monthly payments and annual interest compounded monthly.

D. Incorrect:
- I% = 0.7: Represents the monthly interest rate, and while P/Y and C/Y are both 12, the use of 0.7 would require a context differently set than provided by the problem where 8.4% annual is the driver.

Therefore, option C is the correct choice because it aligns the annual interest rate and the monthly payment compounding structure correctly needed to solve for the number of payments.