Answer :
To determine which group of values can be used in the TVM Solver to calculate the number of payments Kendra will have to make for her loan, let's review her loan details and each of the provided options.
### Kendra's Loan Details
1. Loan Amount (PV): \[tex]$750 (negative because it's a loan she's taking out)
2. Monthly Payment (PMT): \$[/tex]46.50
3. Final Value (FV): \$0 (The loan is fully paid off at the end)
4. Annual Interest Rate (I%): 8.4%
5. Interest Compounded Monthly: The monthly interest rate = 8.4% / 12 months = 0.7%
6. Payments per Year (P/Y): 12 (because she pays monthly)
7. Compounding per Year (C/Y): 12 (because interest is compounded monthly)
8. Payment at the end of each period: PMT:END
### Review the Provided Options
1. Option A:
- N = ; I% = 0.7 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 12 ; C/Y = 12 ; PMT:END
- This option uses the correct monthly interest rate of 0.7%, has the correct loan amount and payment details, and has the correct P/Y and C/Y settings for monthly conditions. This setup matches Kendra's loan details accurately.
2. Option B:
- N = ; I% = 8.4 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 1 ; C/Y = 12 ; PMT:END
- This option uses the annual interest rate directly instead of the monthly rate, and it incorrectly sets P/Y to 1 instead of 12 for monthly payments.
3. Option C:
- N = ; I% = 0.7 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 1 ; C/Y = 12 ; PMT:END
- Although the interest rate is correct at 0.7%, it incorrectly sets P/Y to 1 instead of 12. This doesn't align with monthly payments.
4. Option D:
- N = ; I% = 8.4 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 12 ; C/Y = 12 ; PMT:END
- This incorrectly uses the annual interest rate of 8.4% instead of the monthly rate of 0.7%.
### Conclusion
The correct settings that match all the details of Kendra’s loan are option A. It correctly applies the monthly interest rate, loan amount, payment structure, and monthly settings for both payments and compounding. Therefore, the correct answer is:
A. N=; I%=0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
### Kendra's Loan Details
1. Loan Amount (PV): \[tex]$750 (negative because it's a loan she's taking out)
2. Monthly Payment (PMT): \$[/tex]46.50
3. Final Value (FV): \$0 (The loan is fully paid off at the end)
4. Annual Interest Rate (I%): 8.4%
5. Interest Compounded Monthly: The monthly interest rate = 8.4% / 12 months = 0.7%
6. Payments per Year (P/Y): 12 (because she pays monthly)
7. Compounding per Year (C/Y): 12 (because interest is compounded monthly)
8. Payment at the end of each period: PMT:END
### Review the Provided Options
1. Option A:
- N = ; I% = 0.7 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 12 ; C/Y = 12 ; PMT:END
- This option uses the correct monthly interest rate of 0.7%, has the correct loan amount and payment details, and has the correct P/Y and C/Y settings for monthly conditions. This setup matches Kendra's loan details accurately.
2. Option B:
- N = ; I% = 8.4 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 1 ; C/Y = 12 ; PMT:END
- This option uses the annual interest rate directly instead of the monthly rate, and it incorrectly sets P/Y to 1 instead of 12 for monthly payments.
3. Option C:
- N = ; I% = 0.7 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 1 ; C/Y = 12 ; PMT:END
- Although the interest rate is correct at 0.7%, it incorrectly sets P/Y to 1 instead of 12. This doesn't align with monthly payments.
4. Option D:
- N = ; I% = 8.4 ; PV = -750 ; PMT = 46.5 ; FV = 0 ; P/Y = 12 ; C/Y = 12 ; PMT:END
- This incorrectly uses the annual interest rate of 8.4% instead of the monthly rate of 0.7%.
### Conclusion
The correct settings that match all the details of Kendra’s loan are option A. It correctly applies the monthly interest rate, loan amount, payment structure, and monthly settings for both payments and compounding. Therefore, the correct answer is:
A. N=; I%=0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END