Answer :
To solve this problem, we need to determine which set of values should be used in the TVM (Time Value of Money) Solver on a graphing calculator to find out the number of monthly payments Kendra needs to make.
Let's break down the choices:
1. Understanding the Problem:
- Kendra has taken a loan of [tex]$750.
- The annual percentage rate (APR) is 8.4%.
- Payments are monthly.
- The monthly payment amount is $[/tex]46.50.
- The goal is to pay off the loan completely, meaning the future value (FV) should be [tex]$0 at the end of the payments.
2. Identify Key Values:
- PV (Present Value): Kendra borrowed $[/tex]750, so PV = -750 (the negative sign indicates an outflow of money).
- I% (Interest Rate per Year): 8.4%.
- PMT (Payment per Period): [tex]$46.50.
- FV (Future Value): $[/tex]0, because the loan should be paid off.
- P/Y (Payments per Year): Payments are monthly, so P/Y = 12.
- C/Y (Compounding Periods per Year): Interest is compounded monthly, so C/Y = 12.
- PMT:END: Payments occur at the end of each period.
3. Evaluate Options:
- Option A: Incorrect because P/Y = 1, which suggests yearly payments, but we know payments are monthly.
- Option B: Incorrect because I% is given as 0.7, which would be the monthly rate not the annual rate as required.
- Option C: Incorrect due to P/Y = 1; again, it suggests yearly payments incorrectly.
- Option D: This option correctly handles monthly compounding and payments, with P/Y and C/Y both set to 12. I% is correctly represented as the annual interest rate of 8.4%.
Therefore, the correct group of values to use in the TVM Solver to calculate the number of monthly payments is option D. This setup utilizes the right parameters for monthly payments and compounding, which fits the details given in Kendra's loan situation.
Let's break down the choices:
1. Understanding the Problem:
- Kendra has taken a loan of [tex]$750.
- The annual percentage rate (APR) is 8.4%.
- Payments are monthly.
- The monthly payment amount is $[/tex]46.50.
- The goal is to pay off the loan completely, meaning the future value (FV) should be [tex]$0 at the end of the payments.
2. Identify Key Values:
- PV (Present Value): Kendra borrowed $[/tex]750, so PV = -750 (the negative sign indicates an outflow of money).
- I% (Interest Rate per Year): 8.4%.
- PMT (Payment per Period): [tex]$46.50.
- FV (Future Value): $[/tex]0, because the loan should be paid off.
- P/Y (Payments per Year): Payments are monthly, so P/Y = 12.
- C/Y (Compounding Periods per Year): Interest is compounded monthly, so C/Y = 12.
- PMT:END: Payments occur at the end of each period.
3. Evaluate Options:
- Option A: Incorrect because P/Y = 1, which suggests yearly payments, but we know payments are monthly.
- Option B: Incorrect because I% is given as 0.7, which would be the monthly rate not the annual rate as required.
- Option C: Incorrect due to P/Y = 1; again, it suggests yearly payments incorrectly.
- Option D: This option correctly handles monthly compounding and payments, with P/Y and C/Y both set to 12. I% is correctly represented as the annual interest rate of 8.4%.
Therefore, the correct group of values to use in the TVM Solver to calculate the number of monthly payments is option D. This setup utilizes the right parameters for monthly payments and compounding, which fits the details given in Kendra's loan situation.