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Sagot :
Let's go through the given problem step-by-step and determine which group of values correctly represents the loan situation in a TVM solver on a graphing calculator.
We are given the following conditions:
- A 25-year loan
- An APR of 16.8%
- Payments made monthly
- Monthly payments of [tex]$340 - We aim to fully pay off the loan, meaning the future value (FV) is 0 - Payments are made at the end of each period ### Key Variables in the TVM Solver: 1. N (Number of Periods): This is the total number of payment periods. Since the loan term is 25 years and payments are made monthly, we need to calculate the total number of months: \[ N = 25 \text{ years} \times 12 \text{ months/year} = 300 \text{ months} \] 2. I% (Annual Interest Rate): The annual percentage rate (APR) given is 16.8%. 3. PV (Present Value): This’s the principal amount of the loan that we’re solving for. 4. PMT (Payment Per Period): The monthly payment amount is $[/tex]340, and since it's an outflow, it should be treated as a negative value.
5. FV (Future Value): Since the loan will be completely paid off, the future value is $0.
6. P/Y (Payments Per Year): There are 12 monthly payments in a year, so P/Y = 12.
7. C/Y (Compounding Periods Per Year): Since the interest is compounded monthly, C/Y = 12.
8. PMT: END: This indicates that payments are made at the end of each period.
### Checking Each Group of Values
#### Group A:
- [tex]\( N = 25 \)[/tex]
- [tex]\( I\% = 16.8 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Incorrect: The value for [tex]\( N \)[/tex] is not accounted correctly. It should be in months (300), not years (25).
#### Group B:
- [tex]\( N = 300 \)[/tex]
- [tex]\( I\% = 16.8 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Correct: All values align with the problem's conditions, including\, N \) being 300 months.
#### Group C:
- [tex]\( N = 25 \)[/tex]
- [tex]\( I\% = 1.4 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Incorrect: The annual interest rate [tex]\( I\%) is incorrectly represented as a monthly rate (1.4%). #### Group D: - \( N = 300 \)[/tex]
- [tex]\( I\% = 1.4 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Incorrect: The value for the annual interest rate [tex]\( I\%) is mistaken as 1.4% instead of 16.8%. ### Conclusion The correct group of values for this problem is: B. \( N=300; I \%= 16.8; PV=; PMT=-340; FV=0; P/Y=12; C/Y=12 \)[/tex]; PMT: END
We are given the following conditions:
- A 25-year loan
- An APR of 16.8%
- Payments made monthly
- Monthly payments of [tex]$340 - We aim to fully pay off the loan, meaning the future value (FV) is 0 - Payments are made at the end of each period ### Key Variables in the TVM Solver: 1. N (Number of Periods): This is the total number of payment periods. Since the loan term is 25 years and payments are made monthly, we need to calculate the total number of months: \[ N = 25 \text{ years} \times 12 \text{ months/year} = 300 \text{ months} \] 2. I% (Annual Interest Rate): The annual percentage rate (APR) given is 16.8%. 3. PV (Present Value): This’s the principal amount of the loan that we’re solving for. 4. PMT (Payment Per Period): The monthly payment amount is $[/tex]340, and since it's an outflow, it should be treated as a negative value.
5. FV (Future Value): Since the loan will be completely paid off, the future value is $0.
6. P/Y (Payments Per Year): There are 12 monthly payments in a year, so P/Y = 12.
7. C/Y (Compounding Periods Per Year): Since the interest is compounded monthly, C/Y = 12.
8. PMT: END: This indicates that payments are made at the end of each period.
### Checking Each Group of Values
#### Group A:
- [tex]\( N = 25 \)[/tex]
- [tex]\( I\% = 16.8 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Incorrect: The value for [tex]\( N \)[/tex] is not accounted correctly. It should be in months (300), not years (25).
#### Group B:
- [tex]\( N = 300 \)[/tex]
- [tex]\( I\% = 16.8 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Correct: All values align with the problem's conditions, including\, N \) being 300 months.
#### Group C:
- [tex]\( N = 25 \)[/tex]
- [tex]\( I\% = 1.4 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Incorrect: The annual interest rate [tex]\( I\%) is incorrectly represented as a monthly rate (1.4%). #### Group D: - \( N = 300 \)[/tex]
- [tex]\( I\% = 1.4 \)[/tex]
- [tex]\( PV = \)[/tex]
- [tex]\( PMT = -340 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END
Incorrect: The value for the annual interest rate [tex]\( I\%) is mistaken as 1.4% instead of 16.8%. ### Conclusion The correct group of values for this problem is: B. \( N=300; I \%= 16.8; PV=; PMT=-340; FV=0; P/Y=12; C/Y=12 \)[/tex]; PMT: END
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