Answer :
To find the correct group of values for the TVM (Time Value of Money) Solver to calculate the number of payments Kendra will have to make, we need to ensure that the values reflect the details of the loan accurately. Here's how you can determine the correct values:
1. Understanding the Loan Terms:
- Loan Amount (Present Value, PV) is [tex]$750.
- Annual Percentage Rate (APR) is 8.4%.
- The interest is compounded monthly.
- Monthly payment (PMT) is $[/tex]46.50.
- Future Value (FV) is [tex]$0, because the loan will be fully paid off.
- Payments per year (P/Y) and compounding per year (C/Y) should reflect monthly payments and compounding, so they would both be 12.
2. Converting the Annual Interest Rate:
- Since the APR is 8.4%, and it is compounded monthly, you need to convert this annual rate to a monthly rate.
- Monthly interest rate = 8.4% / 12 = 0.7%.
3. Setting Up the TVM Solver:
- N: This is what we're solving for, the number of payments.
- I%: The interest rate per period (monthly), which is 0.7%.
- PV: Present Value, which is the loan amount. For borrowing, this is typically entered as a negative number because it's an outgoing payment, so PV = -750.
- PMT: Payment made each period, $[/tex]46.50.
- FV: Future Value, set to 0 because the loan will be fully paid off.
- P/Y: Payments per year, which is 12 since payments are made monthly.
- C/Y: Compounding periods per year, which is also 12 for monthly compounding.
- PMT: Set to END, meaning payments are made at the end of each period.
By checking these setups against the options provided, we find:
- Option A reflects the correct use of the monthly interest rate (0.7%) and the correct values for P/Y and C/Y (both 12). This option correctly models monthly payments and compounding.
Therefore, the correct choice is Option A.
1. Understanding the Loan Terms:
- Loan Amount (Present Value, PV) is [tex]$750.
- Annual Percentage Rate (APR) is 8.4%.
- The interest is compounded monthly.
- Monthly payment (PMT) is $[/tex]46.50.
- Future Value (FV) is [tex]$0, because the loan will be fully paid off.
- Payments per year (P/Y) and compounding per year (C/Y) should reflect monthly payments and compounding, so they would both be 12.
2. Converting the Annual Interest Rate:
- Since the APR is 8.4%, and it is compounded monthly, you need to convert this annual rate to a monthly rate.
- Monthly interest rate = 8.4% / 12 = 0.7%.
3. Setting Up the TVM Solver:
- N: This is what we're solving for, the number of payments.
- I%: The interest rate per period (monthly), which is 0.7%.
- PV: Present Value, which is the loan amount. For borrowing, this is typically entered as a negative number because it's an outgoing payment, so PV = -750.
- PMT: Payment made each period, $[/tex]46.50.
- FV: Future Value, set to 0 because the loan will be fully paid off.
- P/Y: Payments per year, which is 12 since payments are made monthly.
- C/Y: Compounding periods per year, which is also 12 for monthly compounding.
- PMT: Set to END, meaning payments are made at the end of each period.
By checking these setups against the options provided, we find:
- Option A reflects the correct use of the monthly interest rate (0.7%) and the correct values for P/Y and C/Y (both 12). This option correctly models monthly payments and compounding.
Therefore, the correct choice is Option A.