a company will need $45,000 in 8 years for a new addition. to meet this goal, the company deposits money in…

a company will need $45,000 in 8 years for a new addition. to meet this goal, the company deposits money in an account today that pays 11% annual interest compounded quarterly. find the amount that should be invested to total $45,000 in 8 years. the company should invest $. (do not round until the final answer. then round to the nearest dollar as needed.)

a company will need $45,000 in 8 years for a new addition. to meet this goal, the company deposits money in an account today that pays 11% annual interest compounded quarterly. find the amount that should be invested to total $45,000 in 8 years. the company should invest $. (do not round until the final answer. then round to the nearest dollar as needed.)

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for present value is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $PV$ is the present value (the amount to be invested today), $FV$ is the future value ($FV = 45000$), $r$ is the annual interest rate ($r=0.11$), $n$ is the number of times compounded per year ($n = 4$ for quarterly compounding), and $t$ is the number of years ($t = 8$).

Step2: Calculate the exponent

First, calculate $(1+\frac{r}{n})^{nt}$. Substitute $r = 0.11$, $n = 4$, and $t = 8$ into the exponent part: $nt=4\times8 = 32$ and $\frac{r}{n}=\frac{0.11}{4}=0.0275$. Then $(1+\frac{r}{n})^{nt}=(1 + 0.0275)^{32}$. Using a calculator, $(1 + 0.0275)^{32}\approx2.39843$.

Step3: Calculate the present value

Now, use the present - value formula $PV=\frac{FV}{(1+\frac{r}{n})^{nt}}$. Substitute $FV = 45000$ and $(1+\frac{r}{n})^{nt}\approx2.39843$ into the formula: $PV=\frac{45000}{2.39843}\approx18762$.

Answer:

$18762$