Question

How much interest will an account earn if you deposited $735 semi-annually for 7 years and the account earned 5.75% compounded semi-annually?$________________Round to the nearest cent

Answer 1

Given:

The interest amount earned is, P = $735.

The number of years is, n = 7.

The rate of interest is, r = 5.75% = 0.0575.

The objective is to find the amount of interest earned.

Step-by-step explanation:

The general formula to find the total amount earned by compount interest is,

`A=P(1+(r)/(n))^(n(t))`

Here, n represents the number of times the interest is compounded per year. It is given that the interest is compounded semi-annually.

So, the value of n = 2.

To find total amount:

Now, substitute the given values in the general formula.

`\begin{gathered} A=735(1+(0.0575)/(2))^(2(7)) \\ =735(1+0.02875)^(14) \\ =1093.01 \end{gathered}`

To find interest amount:

Now, the interest amount can be calculated as,

`\begin{gathered} CI=A-P \\ =1093.01-735 \\ =358.01 \end{gathered}`

Hence, the interest earned is $358.01.