IDNLearn.com offers a reliable platform for finding accurate and timely answers. Our Q&A platform offers reliable and thorough answers to help you make informed decisions quickly and easily.
Sagot :
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.
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.
