Question

Justin deposited $4000 into an account with 5.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have inthe account after 10 years?Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

First, divide the annual interest rate by 2 to find the semiannual interest rate:

`(5.5)/(2)=2.75`

Next, identify the number of periods when the 2.75% increase will be appliad. In a period of 10 years, there are 20 semiannual periods.

Each period, the initial investment gets multiplied by a factor of:

`1+(2.75)/(100)=1+0.0275=1.0275`

Over 20 semiannual periods, the initial investment will get multiplied by a factor of:

`1.0275^(20)`

Therefore, after 10 years, the amount of money in the account is:

`\begin{gathered} 4000*(1.0275)^(20)=4000*1.7204\ldots \\ =6881.7137\ldots \end{gathered}`

To the nearest cent, the amount of money in the account will be:

`6881.71`