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Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the same value for [tex]\(PV\)[/tex] as the expression [tex]\(\frac{(505)\left((1+0.004)^{60}-1\right)}{(0.004)(1+0.004)^{60}}\)[/tex]?

A. [tex]\(N=5\)[/tex]; [tex]\(I\%=4.8\)[/tex]; [tex]\(PV=\)[/tex]; [tex]\(PMT=-505\)[/tex]; [tex]\(FV=0\)[/tex]; [tex]\(P/Y=12\)[/tex]; [tex]\(C/Y=12\)[/tex]; [tex]\(PMT: END\)[/tex]

B. [tex]\(N=60\)[/tex]; [tex]\(I\%=4.8\)[/tex]; [tex]\(PV=\)[/tex]; [tex]\(PMT=-505\)[/tex]; [tex]\(FV=0\)[/tex]; [tex]\(P/Y=12\)[/tex]; [tex]\(C/Y=12\)[/tex]; [tex]\(PMT: END\)[/tex]

C. [tex]\(N=5\)[/tex]; [tex]\(I\%=0.4\)[/tex]; [tex]\(PV=\)[/tex]; [tex]\(PMT=-505\)[/tex]; [tex]\(FV=0\)[/tex]; [tex]\(P/Y=12\)[/tex]; [tex]\(C/Y=12\)[/tex]; [tex]\(PMT: END\)[/tex]

D. [tex]\(N=60\)[/tex]; [tex]\(I\%=0.4\)[/tex]; [tex]\(PV=\)[/tex]; [tex]\(PMT=-505\)[/tex]; [tex]\(FV=0\)[/tex]; [tex]\(P/Y=12\)[/tex]; [tex]\(C/Y=12\)[/tex]; [tex]\(PMT: END\)[/tex]

Sagot :

GinnyAnswer
To determine which group of given values plugged into the TVM (Time Value of Money) Solver matches the present value (PV) calculated by the expression [tex]\(\frac{(5505)\left((1+0.004)^{60}-1\right)}{(0.004)(1+0.004)^{60}}\)[/tex], follow these steps:

1. Expression Analysis:
We have the expression [tex]\(\frac{(5505)\left((1+0.004)^{60}-1\right)}{(0.004)(1+0.004)^{60}}\)[/tex]. This expression is used to find the present value (PV) of a series of payments.

2. Given Options Analysis:
The different options provided for the TVM Solver contain variables typically used in such calculations:
- [tex]\(N\)[/tex] (Number of periods)
- [tex]\(i\%\)[/tex] (Annual interest rate)
- [tex]\(PMT\)[/tex] (Payment amount per period)
- [tex]\(FV\)[/tex] (Future value)
- [tex]\(P/Y\)[/tex] (Payments per year)
- [tex]\(C/Y\)[/tex] (Compounding periods per year)
- [tex]\(PMT: END\)[/tex] (Payments made at the end of each period)

3. Exploring Each Option:
- Option A:
- [tex]\(N = 5\)[/tex]
- [tex]\(i\% = 4.8\)[/tex]
- [tex]\(PMT = -505\)[/tex]
- [tex]\(FV = 0\)[/tex]
- [tex]\(P/Y = 12\)[/tex]
- [tex]\(C/Y = 12\)[/tex]
- [tex]\(PMT: END\)[/tex]

- Option B:
- [tex]\(N = 60\)[/tex]
- [tex]\(i\% = 4.8\)[/tex]
- [tex]\(PMT = -505\)[/tex]
- [tex]\(FV = 0\)[/tex]
- [tex]\(P/Y = 12\)[/tex]
- [tex]\(C/Y = 12\)[/tex]
- [tex]\(PMT: END\)[/tex]

- Option C:
- [tex]\(N = 5\)[/tex]
- [tex]\(i\% = 0.4\)[/tex]
- [tex]\(PMT = -505\)[/tex]
- [tex]\(FV = 0\)[/tex]
- [tex]\(P/Y = 12\)[/tex]
- [tex]\(C/Y = 12\)[/tex]
- [tex]\(PMT: END\)[/tex]

- Option D:
- [tex]\(N = 60\)[/tex]
- [tex]\(i\% = 0.4\)[/tex]
- [tex]\(PMT = -505\)[/tex]
- [tex]\(FV = 0\)[/tex]
- [tex]\(P/Y = 12\)[/tex]
- [tex]\(C/Y = 12\)[/tex]
- [tex]\(PMT: END\)[/tex]

4. Result and Conclusion:
After plugging these values into the TVM Solver or performing appropriate calculations for present value (PV) based on formulas for annuities, it turns out that none of the given options (A, B, C, or D) will return the same value for PV as the expression [tex]\(\frac{(5505)\left((1+0.004)^{60}-1\right)}{(0.004)(1+0.004)^{60}}\)[/tex].

Therefore, the correct answer is:

None of the given options match the present value calculated by the given expression.

Thus, the final answer is:
```
None
```
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