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, let's analyze each option based on the provided loan details:
1. Loan Information:
- Principal (PV): [tex]$750
- Annual Percentage Rate (APR): 8.4%
- Monthly Payment (PMT): $[/tex]46.50
- Future Value (FV): [tex]$0 (since Kendra wants to pay off the loan completely)
- Payments per Year (P/Y): 12 (monthly payments)
- Compounding Periods per Year (C/Y): 12 (monthly compounding)
2. Focus on Interest Rate (i%):
- The annual interest rate is 8.4%, but because the interest is compounded monthly, we need the monthly interest rate.
- The monthly interest rate is calculated by dividing the annual rate by the number of compounding periods per year, which is 12.
- Monthly rate calculation: \( \text{APR} / 12 = 8.4\% / 12 = 0.7\% \) monthly.
3. TVM Solver Settings:
- To find the number of payments (N), you should correctly substitute the values:
- i% (interest rate per period): Since it's compounded monthly, the monthly interest rate is 0.7%.
- PV (Present Value): This is the amount of the loan, so it's -750 (negative because it's an outflow).
- PMT (Payment): The monthly payment is $[/tex]46.50.
- FV (Future Value): Kendra wants to pay it off entirely, so FV is 0.
- P/Y (Payments Per Year): 12, because payments are monthly.
- C/Y (Compounding Periods Per Year): 12, because interest is compounded monthly.
- Payments made at END of period: Typically payments such as these are at the end.
4. Reviewing options:
- Option A: Uses i% = 8.4 and P/Y = 1, which doesn't match the monthly compounding and monthly payment requirement.
- Option B: Uses PV = 750, which is incorrect because it should be negative.
- Option C: Suggests i% = 0.7, PV = -750, PMT = 46.5, FV = 0, P/Y = 12, C/Y = 12, which matches our set conditions.
- Option D: Uses P/Y = 1, which doesn't align with monthly payments.
Option C is the correct set of values to use in the TVM Solver as it correctly reflects monthly interest rate and compounding, with the present value being negative and the payments aligned as monthly.
1. Loan Information:
- Principal (PV): [tex]$750
- Annual Percentage Rate (APR): 8.4%
- Monthly Payment (PMT): $[/tex]46.50
- Future Value (FV): [tex]$0 (since Kendra wants to pay off the loan completely)
- Payments per Year (P/Y): 12 (monthly payments)
- Compounding Periods per Year (C/Y): 12 (monthly compounding)
2. Focus on Interest Rate (i%):
- The annual interest rate is 8.4%, but because the interest is compounded monthly, we need the monthly interest rate.
- The monthly interest rate is calculated by dividing the annual rate by the number of compounding periods per year, which is 12.
- Monthly rate calculation: \( \text{APR} / 12 = 8.4\% / 12 = 0.7\% \) monthly.
3. TVM Solver Settings:
- To find the number of payments (N), you should correctly substitute the values:
- i% (interest rate per period): Since it's compounded monthly, the monthly interest rate is 0.7%.
- PV (Present Value): This is the amount of the loan, so it's -750 (negative because it's an outflow).
- PMT (Payment): The monthly payment is $[/tex]46.50.
- FV (Future Value): Kendra wants to pay it off entirely, so FV is 0.
- P/Y (Payments Per Year): 12, because payments are monthly.
- C/Y (Compounding Periods Per Year): 12, because interest is compounded monthly.
- Payments made at END of period: Typically payments such as these are at the end.
4. Reviewing options:
- Option A: Uses i% = 8.4 and P/Y = 1, which doesn't match the monthly compounding and monthly payment requirement.
- Option B: Uses PV = 750, which is incorrect because it should be negative.
- Option C: Suggests i% = 0.7, PV = -750, PMT = 46.5, FV = 0, P/Y = 12, C/Y = 12, which matches our set conditions.
- Option D: Uses P/Y = 1, which doesn't align with monthly payments.
Option C is the correct set of values to use in the TVM Solver as it correctly reflects monthly interest rate and compounding, with the present value being negative and the payments aligned as monthly.