Answer :
To determine the correct group of values to be used in the TVM (Time Value of Money) Solver of a graphing calculator for calculating the amount of a 25-year loan with an APR of 16.8%, compounded monthly, and paid off with monthly payments of $340, let's examine each option provided:
First, let's break down the necessary values for the TVM Solver:
- N: Total number of payment periods. Since we are making monthly payments for 25 years:
[tex]\[ N = 25 \text{ years} \times 12 \text{ months/year} = 300 \text{ months} \][/tex]
- I%: Annual Interest Rate. Given as 16.8%.
- PV: Present Value. This is the initial loan amount we want to determine.
- PMT: Payment amount. Monthly payment of $340 (considered as an outflow, hence it should be negative):
[tex]\[ PMT = -340 \][/tex]
- FV: Future Value. Since the loan is fully paid off, the amount remaining at the end of the loan term is $0:
[tex]\[ FV = 0 \][/tex]
- P/Y: Payments per year. Given as monthly payments:
[tex]\[ P/Y = 12 \][/tex]
- C/Y: Compounding periods per year. Compounded monthly:
[tex]\[ C/Y = 12 \][/tex]
- PMT: END: Payments are made at the end of each period.
Given these values, let’s evaluate the options:
Option A:
[tex]\[ N=300, I\%=1.4, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
This option shows an annual interest rate of 1.4%, which is incorrect based on the given 16.8% APR. Hence, this option is not valid.
Option B:
[tex]\[ N=300, I\%=16.8, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
All values here match the given conditions, making this the correct setup to determine the present value of the loan.
Option C:
[tex]\[ N=25, I\%=16.8, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
This option incorrectly sets N to 25, which should actually be the number of years multiplied by 12 (totaling 300 months). Hence, this option is incorrect.
Option D:
[tex]\[ N=25, I\%=1.4, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
This option contains errors in both the number of periods (N=25 instead of 300) and the annual interest rate (1.4% instead of 16.8%). Therefore, this is not a valid option.
From the analysis, the correct choice of values for plugging into the TVM Solver is:
Option B:
[tex]\[ N=300, I\%=16.8, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
First, let's break down the necessary values for the TVM Solver:
- N: Total number of payment periods. Since we are making monthly payments for 25 years:
[tex]\[ N = 25 \text{ years} \times 12 \text{ months/year} = 300 \text{ months} \][/tex]
- I%: Annual Interest Rate. Given as 16.8%.
- PV: Present Value. This is the initial loan amount we want to determine.
- PMT: Payment amount. Monthly payment of $340 (considered as an outflow, hence it should be negative):
[tex]\[ PMT = -340 \][/tex]
- FV: Future Value. Since the loan is fully paid off, the amount remaining at the end of the loan term is $0:
[tex]\[ FV = 0 \][/tex]
- P/Y: Payments per year. Given as monthly payments:
[tex]\[ P/Y = 12 \][/tex]
- C/Y: Compounding periods per year. Compounded monthly:
[tex]\[ C/Y = 12 \][/tex]
- PMT: END: Payments are made at the end of each period.
Given these values, let’s evaluate the options:
Option A:
[tex]\[ N=300, I\%=1.4, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
This option shows an annual interest rate of 1.4%, which is incorrect based on the given 16.8% APR. Hence, this option is not valid.
Option B:
[tex]\[ N=300, I\%=16.8, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
All values here match the given conditions, making this the correct setup to determine the present value of the loan.
Option C:
[tex]\[ N=25, I\%=16.8, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
This option incorrectly sets N to 25, which should actually be the number of years multiplied by 12 (totaling 300 months). Hence, this option is incorrect.
Option D:
[tex]\[ N=25, I\%=1.4, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
This option contains errors in both the number of periods (N=25 instead of 300) and the annual interest rate (1.4% instead of 16.8%). Therefore, this is not a valid option.
From the analysis, the correct choice of values for plugging into the TVM Solver is:
Option B:
[tex]\[ N=300, I\%=16.8, PV=0, PMT=-340, FV=0, PY=12, CY=12, PMT:END \][/tex]
