Answer :
To determine the appropriate group of values to plug into the TVM (Time Value of Money) Solver for a graphing calculator for a 20-year loan with an APR of 19.2%, compounded monthly, and paid off with monthly payments of [tex]$510, let’s analyze each option step-by-step:
1. Number of Total Payments (N)
- Since the loan term is 20 years and the payments are made monthly, the total number of payments is:
\[
N = 20 \text{ years} \times 12 \text{ months/year} = 240 \text{ months}
\]
2. Interest Rate Per Period (1%)
- The annual interest rate (APR) is 19.2%. Given that interest is compounded monthly, we need to convert this annual rate to a monthly rate:
\[
\text{Monthly Interest Rate} = \frac{19.2\%}{12} = 1.6\%
\]
3. Present Value (PV)
- We are solving for the present value (PV), which represents the initial loan amount.
4. Payment Per Period (PMT)
- The monthly payment amount is given as $[/tex]510. Since this is an outflow, it is denoted as a negative number:
[tex]\[ PMT = -510 \][/tex]
5. Future Value (FV)
- The future value (FV) at the end of the loan should be 0 because the loan will be fully paid off:
[tex]\[ FV = 0 \][/tex]
6. Payments Per Year (P/Y)
- Payments are made monthly, so the number of payments per year is:
[tex]\[ P/Y = 12 \][/tex]
7. Compounding Periods Per Year (C/Y)
- The interest is compounded monthly, so the number of compounding periods per year is:
[tex]\[ C/Y = 12 \][/tex]
8. Payment Timing (PMT)
- Payments are made at the end of each period. Therefore, we use PMT: END.
Let’s match these parameters with the provided options:
- Option A:
[tex]\[ N=240 ; 1\%=19.2 ; PV= ; PMT=-510 ; FV=0 ; P/Y=12 ; C/Y=12; PMT:END \][/tex]
- This option incorrectly uses the annual interest rate (19.2%) as the interest rate per period.
- Option B:
[tex]\[ N=20 ; 1\%=1.6 ; PV= ; PMT=-510 ; FV=0 ; P/Y=12 ; C/Y=12; PMT:END \][/tex]
- This option incorrectly defines the number of total payments N as 20.
- Option C:
[tex]\[ N=240 ; 1\%=1.6 ; PV= ; PMT=-510 ; FV=0 ; P/Y=12 ; C/Y=12; PMT:END \][/tex]
- This option correctly represents all parameters:
- Total number of payments [tex]\(N = 240\)[/tex]
- Monthly interest rate [tex]\(1\% = 1.6\% \)[/tex]
- Payment per period [tex]\(PMT = -510\)[/tex]
- Future value [tex]\(FV = 0\)[/tex]
- Payments per year [tex]\(P/Y = 12\)[/tex]
- Compounding periods per year [tex]\(C/Y = 12\)[/tex]
- Payment at the end of the period [tex]\(PMT:END\)[/tex]
Thus, the correct choice for the given problem is Option C.
[tex]\[ PMT = -510 \][/tex]
5. Future Value (FV)
- The future value (FV) at the end of the loan should be 0 because the loan will be fully paid off:
[tex]\[ FV = 0 \][/tex]
6. Payments Per Year (P/Y)
- Payments are made monthly, so the number of payments per year is:
[tex]\[ P/Y = 12 \][/tex]
7. Compounding Periods Per Year (C/Y)
- The interest is compounded monthly, so the number of compounding periods per year is:
[tex]\[ C/Y = 12 \][/tex]
8. Payment Timing (PMT)
- Payments are made at the end of each period. Therefore, we use PMT: END.
Let’s match these parameters with the provided options:
- Option A:
[tex]\[ N=240 ; 1\%=19.2 ; PV= ; PMT=-510 ; FV=0 ; P/Y=12 ; C/Y=12; PMT:END \][/tex]
- This option incorrectly uses the annual interest rate (19.2%) as the interest rate per period.
- Option B:
[tex]\[ N=20 ; 1\%=1.6 ; PV= ; PMT=-510 ; FV=0 ; P/Y=12 ; C/Y=12; PMT:END \][/tex]
- This option incorrectly defines the number of total payments N as 20.
- Option C:
[tex]\[ N=240 ; 1\%=1.6 ; PV= ; PMT=-510 ; FV=0 ; P/Y=12 ; C/Y=12; PMT:END \][/tex]
- This option correctly represents all parameters:
- Total number of payments [tex]\(N = 240\)[/tex]
- Monthly interest rate [tex]\(1\% = 1.6\% \)[/tex]
- Payment per period [tex]\(PMT = -510\)[/tex]
- Future value [tex]\(FV = 0\)[/tex]
- Payments per year [tex]\(P/Y = 12\)[/tex]
- Compounding periods per year [tex]\(C/Y = 12\)[/tex]
- Payment at the end of the period [tex]\(PMT:END\)[/tex]
Thus, the correct choice for the given problem is Option C.
