Answer :
To solve this problem, we need to determine which group of values can be appropriately used in a Time Value of Money (TVM) calculator to find out how many payments Kendra will need to make on her loan.
Here’s how to approach the problem step-by-step:
1. Understand the Parameters:
- Kendra borrowed [tex]$750.
- The annual interest rate (APR) is 8.4%.
- Interest is compounded monthly.
- She makes monthly payments of $[/tex]46.50.
- The goal is for the loan to be fully paid off, so Future Value (FV) = 0.
2. Determine Monthly Interest Rate:
- The annual interest rate of 8.4% needs to be converted to a monthly interest rate. To do this, divide the annual rate by 12 (since there are 12 months in a year).
- Monthly interest rate = 8.4% / 12
3. Setup TVM Solver Parameters:
- N: The number of payments (unknown in this case, which is what we are solving for).
- I%: Interest rate per period (monthly rate from step 2).
- PV (Present Value): The amount of the loan ([tex]$750).
- PMT (Payment): The monthly payment amount ($[/tex]46.50).
- FV (Future Value): The amount left to pay when the loan is fully paid off (0, in this case).
- P/Y (Payments per Year): Number of payments per year (12 for monthly payments).
- C/Y (Compounding Periods per Year): Number of times the interest is compounded per year (12, since it’s compounded monthly).
4. Analyze the Choices:
- Choice A: P/Y = 1 means payments per year, which is incorrect as we are making monthly payments. This option is not suitable.
- Choice B: I% is given as 0.7, which represents a monthly interest rate. This is correct as 8.4% annual divided by 12 is 0.7%.
- Choice C: Same as Choice B, but P/Y is 1, which is incorrect.
- Choice D: I% is given as 8.4%, which would be the annual rate not monthly. Therefore, it doesn't have a correct setting for monthly interest calculation.
5. Conclusion:
The group of values in Choice B is correctly set up for the given scenario because it uses the correct monthly interest rate, PMT, PV, payments per year, and compounding periods per year settings.
Thus, the solution to the problem is Choice B.
Here’s how to approach the problem step-by-step:
1. Understand the Parameters:
- Kendra borrowed [tex]$750.
- The annual interest rate (APR) is 8.4%.
- Interest is compounded monthly.
- She makes monthly payments of $[/tex]46.50.
- The goal is for the loan to be fully paid off, so Future Value (FV) = 0.
2. Determine Monthly Interest Rate:
- The annual interest rate of 8.4% needs to be converted to a monthly interest rate. To do this, divide the annual rate by 12 (since there are 12 months in a year).
- Monthly interest rate = 8.4% / 12
3. Setup TVM Solver Parameters:
- N: The number of payments (unknown in this case, which is what we are solving for).
- I%: Interest rate per period (monthly rate from step 2).
- PV (Present Value): The amount of the loan ([tex]$750).
- PMT (Payment): The monthly payment amount ($[/tex]46.50).
- FV (Future Value): The amount left to pay when the loan is fully paid off (0, in this case).
- P/Y (Payments per Year): Number of payments per year (12 for monthly payments).
- C/Y (Compounding Periods per Year): Number of times the interest is compounded per year (12, since it’s compounded monthly).
4. Analyze the Choices:
- Choice A: P/Y = 1 means payments per year, which is incorrect as we are making monthly payments. This option is not suitable.
- Choice B: I% is given as 0.7, which represents a monthly interest rate. This is correct as 8.4% annual divided by 12 is 0.7%.
- Choice C: Same as Choice B, but P/Y is 1, which is incorrect.
- Choice D: I% is given as 8.4%, which would be the annual rate not monthly. Therefore, it doesn't have a correct setting for monthly interest calculation.
5. Conclusion:
The group of values in Choice B is correctly set up for the given scenario because it uses the correct monthly interest rate, PMT, PV, payments per year, and compounding periods per year settings.
Thus, the solution to the problem is Choice B.