Question

use the appropriate compound interest formula to compute the balance in the account after the stated period of time $18,000 is invested for 5 years with an APR of 6% and daily compounding.

Answer 1

Given:

a.) Principal amount = $18,000

b.) Time of investment = 5 yrs.

c.) APR (Annual Percentage Rate) = 6%

d.) Compounded daily, n = 365

Let's determine the balance after the given amount of time, we will be using the following formula:

$\text{ A = P(}1\text{ + }\frac{\frac{r}{100}}{n})^{nt}$

Let's plug in the given the data:

$\text{ A = P(}1\text{ + }\frac{\frac{r}{100}}{n})^{nt}$$\text{= (18,000)(}1\text{ + }\frac{\frac{6}{100}}{365})^{365\text{ x 5}}$$\text{ = }(18,000)(1\text{ + }\frac{0.06}{365})^{1,825}$$\text{ = }(18,000)(1\text{ + }0.00016)^{1,825}$$\text{ = }(18,000)(1.00016)^{1,825}$$\text{ = (18,000)(}1.33907)$$\text{ A = \ }24,103.26$

Therefore, the balance of the account will be $24,103.26 in 5 years.