Let's carefully analyze the details needed to determine which set of values will yield the same present value (PV) using a Time Value of Money (TVM) solver on a graphing calculator.
Given formula:
[tex]\[
PV = \frac{(\$ 415)\left((1+0.003)^{24}-1\right)}{(0.003)(1+0.003)^{24}}
\][/tex]
Here is the provided set of values for the TVM solver:
- [tex]\( N = 24 \)[/tex]
- [tex]\( I\% = 0.3 \)[/tex] (annual interest rate)
- [tex]\( PV = ? \)[/tex]
- [tex]\( PMT = -415 \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y \)[/tex] (payments per year) = 12
- [tex]\( C/Y \)[/tex] (compounding periods per year) = 12
- [tex]\( PMT : END \)[/tex] (payments are made at the end of each period)
Now let's analyze the options provided:
A. [tex]\(N=24 ; I\%=0.3 ; PV= ; PMT=-415 ; FV=0 ; P/Y=12 ; C/Y=12 ; PMT:END\)[/tex]
- This matches the setup correctly with [tex]\( I \% \)[/tex] as 0.3% annual interest, 12 payments per year, and 12 compounding periods per year.
- [tex]\(N = 24\)[/tex] periods (months)
- Payments made at the end of each period
- Value of [tex]\( PV \)[/tex] is to be determined.
B. [tex]\(N=2 ; I\%=3.6 ; PV= ; PMT=-415 ; FV=0 ; P/Y=12 ; C/Y=12 ; PMT:END\)[/tex]
- Here [tex]\(I\% = 3.6\% \)[/tex] annual interest and the number of periods [tex]\(N = 2\)[/tex]
- This setup is incorrect because the number of periods [tex]\(N\)[/tex] must be 24 and not 2.
C. [tex]\(N=2 ; I\%=0.3 ; PV= ; PMT=-415 ; FV=0 ; P/Y=12 ; C/Y=12 ; PMT:END\)[/tex]
- In this case, [tex]\(I\% = 0.3\%\)[/tex] annual interest but the number of periods [tex]\(N = 2\)[/tex] is wrong.
- Again, this does not match since [tex]\(N\)[/tex] should be 24 and not 2.
D. [tex]\(N=24 ; I\%=3.6 ; PV= ; PMT=-415 ; FV=0 ; P/Y=12 ; C/Y=12 ; PMT:END\)[/tex]
- [tex]\(I\% = 3.6\%\)[/tex] annual interest rate is not correct, since the interest should be 0.3% annual rate.
- Number of periods [tex]\(N = 24\)[/tex] is correct but the interest rate does not match.
After analyzing each option, it becomes clear that option A:
[tex]\[
N=24 ; I\%=0.3 ; PV= ; PMT=-415 ; FV=0 ; P/Y=12 ; C/Y=12 ; PMT:END
\][/tex]
matches the setup required to yield the same present value as the given formula expression.
Thus the correct group of values is A.
