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 $40,000 after 14 years invested in an account with 4.7% interest compounded monthly. the amount to be invested now, or the present value needed, is $ (round to the nearest cent as needed.) the present value formula is $p=\frac{a}{(1 + \frac{r}{n})^{nt}}$, where $p$ is the present value, or the principal to invest now, $a$ is the amount to be accumulated in the account, $r$ is the annual interest rate as a decimal number, $n$ is the number of compounding periods per year, and $t$ is the time in years.
Answer
Answer:
$19777.03$
Explanation:
Step1: Identify values
$A = 40000$, $r=0.047$, $n = 12$, $t = 14$
Step2: Substitute into formula
$p=\frac{A}{(1 +\frac{r}{n})^{nt}}=\frac{40000}{(1+\frac{0.047}{12})^{12\times14}}$
Step3: Calculate exponent
$(1+\frac{0.047}{12})^{12\times14}=(1+\frac{0.047}{12})^{168}\approx2.0224$
Step4: Calculate present - value
$p=\frac{40000}{2.0224}\approx19777.03$