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

B. [tex]N=; I\%=0.7; 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, we need to set up the key parameters for the Time Value of Money (TVM) calculation.

1. Kendra took a loan of \[tex]$750 at an annual percentage rate (APR) of 8.4%. Since interest is compounded monthly, the periodic (monthly) interest rate is
$[/tex][tex]$
\text{Monthly Interest Rate} = \frac{8.4\%}{12} = 0.7\%.
$[/tex][tex]$

2. The TVM solver inputs must reflect the monthly rate and monthly payments. Therefore:
- The periodic interest rate should be set to $[/tex]0.7\%[tex]$ (not $[/tex]8.4\%[tex]$).
- Since payments are made monthly, the number of payment periods per year should be $[/tex]12[tex]$. Thus, both the number of payments per year ($[/tex]P/Y[tex]$) and the compounding periods per year ($[/tex]C/Y[tex]$) should be 12.
- The present value ($[/tex]PV[tex]$) of the loan should be entered as \$[/tex]-750 (negative because it is an outflow).
- The monthly payment ([tex]$PMT$[/tex]) is \[tex]$46.50.
- The future value ($[/tex]FV[tex]$) is 0, because the loan is to be completely paid off.

3. Reviewing the available options:
- Option A sets the periodic rate as $[/tex]8.4\%[tex]$ and $[/tex]P/Y = 1[tex]$, which does not correctly reflect monthly compounding and payments.
- Option B sets the periodic rate as $[/tex]0.7\%[tex]$, but uses $[/tex]P/Y = 1[tex]$, which is incorrect.
- Option C sets $[/tex]P/Y = 12[tex]$, $[/tex]C/Y = 12[tex]$, but uses a periodic rate of $[/tex]8.4\%[tex]$ instead of $[/tex]0.7\%[tex]$.
- Option D correctly sets the periodic rate to $[/tex]0.7\%[tex]$, with both $[/tex]P/Y = 12[tex]$ and $[/tex]C/Y = 12[tex]$, along with $[/tex]PV=-750[tex]$, $[/tex]PMT=46.5[tex]$, and $[/tex]FV=0[tex]$.

Thus, the correct choice is:

$[/tex][tex]$\boxed{D}$[/tex]$