use the present value formula to determine the amount to be invested now, or the present value needed. the…

use the present value formula to determine the amount to be invested now, or the present value needed. the desired accumulated amount is $30,000 after 14 years invested in an account with 5.3% interest compounded monthly. the amount to be invested now, or the present value needed, is $ (round to the nearest cent as needed.)

use the present value formula to determine the amount to be invested now, or the present value needed. the desired accumulated amount is $30,000 after 14 years invested in an account with 5.3% interest compounded monthly. the amount to be invested now, or the present value needed, is $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the compound - interest formula for present value

The compound - interest formula for present value $PV$ is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $FV$ is the future value, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

We are given that $FV = 30000$, $r=0.053$ (since $5.3%=0.053$), $n = 12$ (compounded monthly), and $t = 14$.

Step3: Substitute the values into the formula

[ \begin{align*} PV&=\frac{30000}{(1+\frac{0.053}{12})^{12\times14}}\ &=\frac{30000}{(1 + 0.0044167)^{168}}\ &=\frac{30000}{(1.0044167)^{168}} \end{align*} ] Calculate $(1.0044167)^{168}\approx2.05777$. Then $PV=\frac{30000}{2.05777}\approx14579.67$.

Answer:

$14579.67$