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 $110,000 after 4 years invested in an account with 2% interest compounded quarterly. the amount to be invested now, or the present value needed, is $101,563.04. (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 $110,000 after 4 years invested in an account with 2% interest compounded quarterly. the amount to be invested now, or the present value needed, is $101,563.04. (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify compound - interest formula

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

Step2: Convert given values to appropriate form

We have $FV = 110000$, $r=0.02$ (since $2%=0.02$), $n = 4$ (compounded quarterly), and $t = 4$.

Step3: Substitute values into the formula

$PV=\frac{110000}{(1+\frac{0.02}{4})^{4\times4}}=\frac{110000}{(1 + 0.005)^{16}}$.

Step4: Calculate the denominator

$(1 + 0.005)^{16}=1.005^{16}$. Using a calculator, $1.005^{16}\approx1.083075$.

Step5: Calculate the present value

$PV=\frac{110000}{1.083075}\approx101563.04$.

Answer:

$101563.04$