Mathematics

Question

Which of these groups of values plugged into the TVM Solver of a graphing
calculator will return the same value for PV as the expression
($415)((1 +0.003)24 – 1)?
(0.003)(1 +0.003)24
Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the same value for PV as the expression ($415)((1 +0.003)24 – 1

1 Answer

  • 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

    Learn more about Present Value Solver here:

    https://brainly.com/question/1759639

    https://brainly.com/question/13573265

NEWS TODAY