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 13 years invested in an account with 2.2% 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.

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 13 years invested in an account with 2.2% 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

Explanation:

Step1: Identify the values

$A = 50000$, $r=0.022$, $n = 12$ (monthly compounding), $t = 13$

Step2: Substitute into the present - value formula

$p=\frac{A}{(1 +\frac{r}{n})^{nt}}=\frac{50000}{(1+\frac{0.022}{12})^{12\times13}}$

Step3: Calculate the exponent

$12\times13 = 156$, $\frac{0.022}{12}\approx0.001833$ $1+\frac{0.022}{12}=1 + 0.001833=1.001833$ $(1.001833)^{156}\approx1.32077$

Step4: Calculate the present value

$p=\frac{50000}{1.32077}\approx37856.67$

Answer:

$37856.67$