The TVM solver is a tool found in graphing calculators, that solve Time
Value of Money problems.
- The group of values that will return the same value as the given expression is; D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END
Reasons:
In the TVM solver, we have;
I = The annual percentage rate
N = n × t
t = The number of years
PV = Present value
PMT = Payment
P/Y = Number of payments per year = n
C/Y = Number of compounding periods per year = n
The formula for monthly payment is presented as follows;
[tex]M = \mathbf{\dfrac{P \cdot \left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n \times t} }{\left(1+\dfrac{r}{n} \right)^{n \times t} - 1}}[/tex]
Which gives;
[tex]P = \mathbf{\displaystyle \frac{M\cdot \left(\left(1+\dfrac{r}{n} \right)^{n \times t} - 1 \right) }{\left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n \times t}}}[/tex]
Therefore, we get;
Where;
M = PMT = -415
P = PV
r = I
P/Y = n = 12
Therefore;
[tex]\displaystyle 0.003 = \frac{I}{12}[/tex]
I = 0.003 × 12 = 0.036 = 3.6%
N = n × t = 24
[tex]P = \displaystyle \frac{(415)\cdot \left(\left(1+\dfrac{I}{12} \right)^{24} - 1 \right) }{\left(\dfrac{I}{12} \right) \cdot \left(1+\dfrac{I}{12} \right)^{24}} = \mathbf{\displaystyle \frac{(415)\cdot \left(\left(1+0.003\right)^{24} - 1 \right) }{\left(0.003\right) \cdot \left(1+0.003 \right)^{24}}} = ?[/tex]
The value of the equation is the present value, PV = ?
When payment are made based on the PV, we have FV = 0
The group of values the same value as the expression[tex]\displaystyle \frac{(\$415)\cdot (1 + 0.003)^{24} - 1}{(0.003) \cdot (1 + 0.003)^{24}}[/tex], when plugged into the TVM solver of a calculator is; D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END
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