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=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\%=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 :

We are given a loan of \[tex]$750 at an annual rate of $[/tex]8.4\%[tex]$, compounded monthly. When using a TVM (Time Value of Money) solver, it is important to use the interest rate per period rather than the annual rate. Since the interest is compounded monthly, the periodic (monthly) interest rate is calculated by dividing the annual rate by the number of compounding periods per year:

$[/tex][tex]$
\text{Monthly interest rate} = \frac{8.4\%}{12} = 0.7\%
$[/tex][tex]$

The TVM solver should therefore have:
- The interest rate per period ($[/tex]I\%[tex]$) set to $[/tex]0.7\%[tex]$.
- The number of payments per year ($[/tex]P/Y[tex]$) should be $[/tex]12[tex]$.
- The present value ($[/tex]PV[tex]$) input should be $[/tex]-750[tex]$, indicating money borrowed.
- The payment ($[/tex]PMT[tex]$) is set to \$[/tex]46.50.
- The future value ([tex]$FV$[/tex]) is [tex]$0$[/tex], since the loan is paid off.
- The payments are made at the end of each period.

Looking at the options provided:

- Option A uses [tex]$I\% = 8.4$[/tex] which is incorrect since it is the annual rate.
- Option B correctly uses [tex]$I\% = 0.7$[/tex], [tex]$PV = -750$[/tex], [tex]$PMT = 46.5$[/tex], [tex]$FV = 0$[/tex], and [tex]$P/Y = C/Y = 12$[/tex], with payments at the end.
- Option C has the incorrect payment frequency ([tex]$P/Y = 1$[/tex]).
- Option D uses [tex]$I\% = 8.4$[/tex] and the wrong [tex]$P/Y$[/tex], so it is also incorrect.

Thus, the correct choice is Option B.

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