Question

What is the compound interest for a $200 principal invested for 6 years at an interest rate of 9%?

Answer 1

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 = `color(green)(" "9/100 rArr 0.09)`

[ t ] Period (in Years) = `color(green)(" "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`

`rArr 200*(1.09)^6`

`~~200*1.677`

`~~335.4200`

`~~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.