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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]$\[tex]$46.50$[/tex][/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 \, ; \, PMT: END[/tex]

B. [tex]N = \, ; \, I\% = 8.4 \, ; \, PV = -750 \, ; \, PMT = 46.5 \, ; \, FV = 0 \, ; \, P/Y = 12 \, ; \, C/Y = 12 \, ; \, PMT: END[/tex]

C. [tex]N = \, ; \, I\% = 0.7 \, ; \, PV = -750 \, ; \, PMT = 46.5 \, ; \, FV = 0 \, ; \, P/Y = 1 \, ; \, C/Y = 12 \, ; \, PMT: END[/tex]

D. [tex]N = \, ; \, I\% = 0.7 \, ; \, PV = -750 \, ; \, PMT = 46.5 \, ; \, FV = 0 \, ; \, P/Y = 12 \, ; \, C/Y = 12 \, ; \, PMT: END[/tex]



Answer :

GinnyAnswer
To determine which group of values can be used in the TVM (Time-Value of Money) Solver for calculating the number of payments Kendra has to make on her loan, we need to understand the context and meaning of each parameter used in the solver:

- [tex]\( N \)[/tex]: The number of payments Kendra will make. This needs to be determined.
- [tex]\( I\% \)[/tex]: The annual interest rate. Since the loan is compounded monthly, we should use a monthly interest rate in our calculations.
- [tex]\( PV \)[/tex]: The present value of the loan, which is -750 dollars because it represents a loan or debt (outflow of money).
- [tex]\( PMT \)[/tex]: The monthly payment, which is 46.50 dollars.
- [tex]\( FV \)[/tex]: The future value, which is 0 because Kendra will have paid off the loan.
- [tex]\( P/Y \)[/tex]: Payments per year, which in this case, is monthly (12 payments per year).
- [tex]\( C/Y \)[/tex]: Compounding periods per year. Since the interest is compounded monthly, there are 12 compounding periods per year.

Let's go through the given options:

Option A:
- [tex]\( N \)[/tex]: (To be determined)
- [tex]\( I\% \)[/tex]: 8.4
- [tex]\( PV \)[/tex]: -750
- [tex]\( PMT \)[/tex]: 46.5
- [tex]\( FV \)[/tex]: 0
- [tex]\( P/Y \)[/tex]: 1
- [tex]\( C/Y \)[/tex]: 12
- PMT: END

In this option, the annual interest rate is correct (8.4%), but the payments per year (P/Y) is incorrect. It should be 12 since payments are made monthly.

Option B:
- [tex]\( N \)[/tex]: (To be determined)
- [tex]\( I\% \)[/tex]: 8.4
- [tex]\( PV \)[/tex]: -750
- [tex]\( PMT \)[/tex]: 46.5
- [tex]\( FV \)[/tex]: 0
- [tex]\( P/Y \)[/tex]: 12
- [tex]\( C/Y \)[/tex]: 12
- PMT: END

This option correctly specifies 8.4% for the annual interest rate, and both payments per year (P/Y) and compounding periods (C/Y) are set to 12. This is appropriate for monthly payments and monthly compounding.

Option C:
- [tex]\( N \)[/tex]: (To be determined)
- [tex]\( I\% \)[/tex]: 0.7
- [tex]\( PV \)[/tex]: -750
- [tex]\( PMT \)[/tex]: 46.5
- [tex]\( FV \)[/tex]: 0
- [tex]\( P/Y \)[/tex]: 1
- [tex]\( C/Y \)[/tex]: 12
- PMT: END

In this option, the interest rate is incorrectly set to 0.7% per month (8.4% annually/12 months), but the payments per year (P/Y) is incorrect. It should be 12 since payments are made monthly.

Option D:
- [tex]\( N \)[/tex]: (To be determined)
- [tex]\( I\% \)[/tex]: 0.7
- [tex]\( PV \)[/tex]: -750
- [tex]\( PMT \)[/tex]: 46.5
- [tex]\( FV \)[/tex]: 0
- [tex]\( P/Y \)[/tex]: 12
- [tex]\( C/Y \)[/tex]: 12
- PMT: END

This option correctly adjusts the interest rate to the monthly interest rate (0.7%, which is 8.4% annually divided by 12). The payments per year (P/Y) and compounding periods (C/Y) are correctly set to 12.

After analyzing the options, the best group that can be used to calculate the number of payments accurately is:

Option D:
- [tex]\( N \)[/tex]: (To be determined)
- [tex]\( I\% \)[/tex]: 0.7
- [tex]\( PV \)[/tex]: -750
- [tex]\( PMT \)[/tex]: 46.5
- [tex]\( FV \)[/tex]: 0
- [tex]\( P/Y \)[/tex]: 12
- [tex]\( C/Y \)[/tex]: 12
- PMT: END

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