# A company will need $65,000 in 6 years for a new addition. To meet this goal the company deposits money in an account today that pays 5% annual intrest compound quarterly. Find the amount that should be invested to total $65,000 in 6 years.

the company should invest?

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## To find the amount that should be invested to total $65,000 in 6 years, we can use the formula for compound interest:

\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]

Where:

A = the future value of the investment

P = the principal amount (the initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times that interest is compounded per year

t = the number of years

In this case, the principal amount (P) is what we need to find. The future value (A) is given as $65,000. The annual interest rate (r) is 5% or 0.05, and the interest is compounded quarterly, so n is 4. The investment period (t) is 6 years.

Let's plug in these values into the formula and solve for P:

\[\$65,000 = P \left(1 + \frac{0.05}{4}\right)^{(4 \times 6)}\]

Now, we can simplify the equation and solve for P:

\[\$65,000 = P(1.0125)^{24}\]

To isolate P, divide both sides of the equation by \((1.0125)^{24}\):

\[\frac{\$65,000}{(1.0125)^{24}} = P\]

Using a calculator, we get:

\[\frac{\$65,000}{(1.0125)^{24}} \approx \$45,736.676\]

Therefore, the company should invest approximately $45,736.68 to have $65,000 in 6 years.