Answer :
To find out how many payments Kendra will need to make, we need to use the TVM (Time Value of Money) Solver on a graphing calculator. Let's examine the values that need to be entered based on the options provided.
First, let's understand what each variable stands for in the TVM Solver:
- N: The number of payments to be made.
- I%: The annual interest rate as a percentage.
- PV: The present value or the initial amount of the loan (entered as a negative number because it represents an outflow).
- PMT: The payment per period (monthly payment in this case).
- FV: The future value of the loan, which will be zero because the loan will be paid off by the end of the term.
- P/Y: Payments per year.
- C/Y: Compounding periods per year.
- PMT:END: This means payments are made at the end of each period.
Given that Kendra's loan has an 8.4% APR compounded monthly, let's analyze which option is correct:
### Option Analysis:
1. Option A:
- I% = 8.4: Correct for annual interest rate.
- P/Y = 1 and C/Y = 12: The number of payments per year does not match monthly compounding, as P/Y should be 12.
- Therefore, Option A is incorrect.
2. Option B:
- I% = 8.4: Correct for the annual interest rate.
- P/Y = 12 and C/Y = 12: Both are correctly set for monthly payments and monthly compounding.
- Therefore, Option B correctly captures the scenario.
3. Option C:
- I% = 0.7: This suggests a monthly interest rate, which contradicts the given APR format of annual rate.
- P/Y = 12 and C/Y = 12: Correct for monthly payments and compounding.
- Using a monthly interest rate format here does not match the question's context, so it's not suitable for finding the number of payments accurately.
4. Option D:
- I% = 0.7: Like Option C, this implies a monthly interest rate.
- P/Y = 1 and C/Y = 12: Incorrect settings for monthly payments and compounding.
- Therefore, Option D is incorrect.
The correct set of values that correspond to Kendra's scenario and will yield the calculated number of payments she must make is found in Option B.
First, let's understand what each variable stands for in the TVM Solver:
- N: The number of payments to be made.
- I%: The annual interest rate as a percentage.
- PV: The present value or the initial amount of the loan (entered as a negative number because it represents an outflow).
- PMT: The payment per period (monthly payment in this case).
- FV: The future value of the loan, which will be zero because the loan will be paid off by the end of the term.
- P/Y: Payments per year.
- C/Y: Compounding periods per year.
- PMT:END: This means payments are made at the end of each period.
Given that Kendra's loan has an 8.4% APR compounded monthly, let's analyze which option is correct:
### Option Analysis:
1. Option A:
- I% = 8.4: Correct for annual interest rate.
- P/Y = 1 and C/Y = 12: The number of payments per year does not match monthly compounding, as P/Y should be 12.
- Therefore, Option A is incorrect.
2. Option B:
- I% = 8.4: Correct for the annual interest rate.
- P/Y = 12 and C/Y = 12: Both are correctly set for monthly payments and monthly compounding.
- Therefore, Option B correctly captures the scenario.
3. Option C:
- I% = 0.7: This suggests a monthly interest rate, which contradicts the given APR format of annual rate.
- P/Y = 12 and C/Y = 12: Correct for monthly payments and compounding.
- Using a monthly interest rate format here does not match the question's context, so it's not suitable for finding the number of payments accurately.
4. Option D:
- I% = 0.7: Like Option C, this implies a monthly interest rate.
- P/Y = 1 and C/Y = 12: Incorrect settings for monthly payments and compounding.
- Therefore, Option D is incorrect.
The correct set of values that correspond to Kendra's scenario and will yield the calculated number of payments she must make is found in Option B.