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 with the details of Kendra’s loan:

1. The loan amount is \[tex]$750. In the TVM (Time Value of Money) setup, the Present Value (PV) is entered as \$[/tex]-750 (the negative sign indicates a cash outflow).

2. The Annual Percentage Rate (APR) is given as 8.4%. Since the interest is compounded monthly, we must first determine the monthly interest rate. There are 12 months in a year, so the interest rate per month is

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

3. Kendra will make monthly payments of \[tex]$46.50. In the TVM Solver, the Payment (PMT) is entered as \$[/tex]46.50.

4. Since the loan is paid off completely, the Future Value (FV) is \[tex]$0.

5. The payments occur monthly. Therefore, the number of payments per year (P/Y) is 12. Also, because the interest compounds monthly, the number of compounding periods per year (C/Y) is also 12.

Now, when setting up the TVM Solver, the key values are:

- $[/tex]I\% = 0.7\%[tex]$ (monthly interest rate)
- $[/tex]PV = -750[tex]$
- $[/tex]PMT = 46.5[tex]$
- $[/tex]FV = 0[tex]$
- $[/tex]P/Y = 12[tex]$
- $[/tex]C/Y = 12[tex]$

Looking at the answer choices, the option that uses $[/tex]I\% = 0.7[tex]$, $[/tex]P/Y = 12[tex]$, and $[/tex]C/Y = 12$ with the other values correctly entered is:

Option B.

Thus, the correct answer is Option B.