# 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?

## 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.