# What is the compound interest for a $200 principal invested for 6 years at an interest rate of 9%? ##### 1 Answer Jan 25, 2018 #### Answer: Amount (Principal Amount + Interest) = color(blue)($335.42)

Your deposit $200 pays 9 percent interest (0.09) annually. At the end of 6 years, your balance will have grown to$335.42.

#### Explanation:

Given:

[ P ] Principal Amount (Initial Deposit) = color(green)(" "$500.00) [ r ] Rate of Interest = $\textcolor{g r e e n}{\text{ } \frac{9}{100} \Rightarrow 0.09}$[ t ] Period (in Years) = $\textcolor{g r e e n}{\text{ } 6}$[ n ] Number of times the interest is compounded/year = color(green)(" "1 I am assuming that the interest is compounded once annually. We must now find [ A ] Amount accumulated after "n" years, including interest and also the Compound Interest earned/paid We will use the following formula to find Amount [ A ] Amount [ A ] color(blue)(= P[1+(r/n)]^(nt) Using the values given in the problem, we get Amount = 200[1+(0.09/1)]^(1*6 $\Rightarrow 200 \cdot {\left(1.09\right)}^{6}$$\approx 200 \cdot 1.677$$\approx 335.4200$$\approx 335.42$Hence, if your deposit of$200 pays 9 percent interest (0.09) annually, and you keep the deposit for 6 years, at the end of six years, your balance will have grown to \$335.42.