Answer :
To solve this problem, we need to use a financial tool called a TVM (Time Value of Money) Solver, which is commonly found on graphing calculators. The goal is to calculate the number of payments Kendra will need to make to pay off her loan.
Here's how to determine which option is correct:
1. Identifying the Key Parameters:
- Loan Amount (Present Value, PV): Kendra took out a loan of [tex]$750. In TVM terms, money going out is typically labeled as negative, so PV = -750.
- Annual Percentage Rate (I%): The loan has an APR of 8.4%. This is the annual interest rate.
- Monthly Payment (PMT): Kendra makes monthly payments of $[/tex]46.50.
- Future Value (FV): When the loan is entirely paid off, the future value will be $0.
- Compounding and Payment Frequency:
- Payments per Year (P/Y): Since payments are made monthly, P/Y = 12.
- Compounding per Year (C/Y): The problem states the rate is compounded monthly, so C/Y = 12.
- Number of Payments (N): This is what we are solving for.
2. Examining the Options:
- Option A:
- N = (unknown)
- I% = 8.4 (correctly uses the annual interest rate)
- PV = -750 (correctly represents the loan as an outflow)
- PMT = 46.5 (correct monthly payment)
- FV = 0 (goal is to completely pay off the loan)
- P/Y = 12 (correctly indicates monthly payments)
- C/Y = 12 (correctly indicates monthly compounding)
- Option B:
- This option incorrectly uses P/Y = 1, which would imply payments are made annually rather than monthly.
- Option C:
- I% = 0.7, which represents a monthly interest rate rather than the required annual rate in this context.
- Option D:
- Similar to Option C, it uses an incorrect monthly interest rate and the wrong payment frequency.
3. Conclusion:
Option A correctly sets up the TVM Solver with an annual interest rate of 8.4%, monthly payments and compounding, and all other parameters correctly matching the problem's requirements. Therefore, Option A is the correct choice to calculate the number of payments Kendra will need to make to pay off her loan.
So, the answer is Option A.
Here's how to determine which option is correct:
1. Identifying the Key Parameters:
- Loan Amount (Present Value, PV): Kendra took out a loan of [tex]$750. In TVM terms, money going out is typically labeled as negative, so PV = -750.
- Annual Percentage Rate (I%): The loan has an APR of 8.4%. This is the annual interest rate.
- Monthly Payment (PMT): Kendra makes monthly payments of $[/tex]46.50.
- Future Value (FV): When the loan is entirely paid off, the future value will be $0.
- Compounding and Payment Frequency:
- Payments per Year (P/Y): Since payments are made monthly, P/Y = 12.
- Compounding per Year (C/Y): The problem states the rate is compounded monthly, so C/Y = 12.
- Number of Payments (N): This is what we are solving for.
2. Examining the Options:
- Option A:
- N = (unknown)
- I% = 8.4 (correctly uses the annual interest rate)
- PV = -750 (correctly represents the loan as an outflow)
- PMT = 46.5 (correct monthly payment)
- FV = 0 (goal is to completely pay off the loan)
- P/Y = 12 (correctly indicates monthly payments)
- C/Y = 12 (correctly indicates monthly compounding)
- Option B:
- This option incorrectly uses P/Y = 1, which would imply payments are made annually rather than monthly.
- Option C:
- I% = 0.7, which represents a monthly interest rate rather than the required annual rate in this context.
- Option D:
- Similar to Option C, it uses an incorrect monthly interest rate and the wrong payment frequency.
3. Conclusion:
Option A correctly sets up the TVM Solver with an annual interest rate of 8.4%, monthly payments and compounding, and all other parameters correctly matching the problem's requirements. Therefore, Option A is the correct choice to calculate the number of payments Kendra will need to make to pay off her loan.
So, the answer is Option A.