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 $50,000 after 12 years invested in an account with 7.1% 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 $50,000 after 12 years invested in an account with 7.1% 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 $FV = 50000$, $r=0.071$ (since $7.1%=0.071$), $n = 12$ (compounded monthly), and $t = 12$.

Step3: Substitute the values into the formula

$PV=\frac{50000}{(1+\frac{0.071}{12})^{12\times12}}$. First, calculate the value inside the parentheses: $\frac{0.071}{12}\approx0.0059167$, then $1+\frac{0.071}{12}\approx1.0059167$. Next, calculate the exponent: $12\times12 = 144$. So, $(1.0059167)^{144}\approx2.30797$. Then, $PV=\frac{50000}{2.30797}\approx21663.47$.

Answer:

$21663.47$