Question

To save money for a future house, a couple places $4,000 in an interest bearing savings account every month. The account pays 9% annual interest, compounded monthly. How much will the account be worth 8 years after it is opened (to the nearest cent)?

Answer 1

The formula to calculate the amount after being compounded is given below as

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ P=4000 \\ r=9\%=(9)/(100)=0.09 \\ n=12 \\ t=8 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=4000(1+(0.09)/(12))^(12*8) \\ A=4000(1+0.0075)^(96) \\ A=4000(1.0075)^(96) \\ A=8195.68 \end{gathered}`

Hence,

The final answer is

`\Rightarrow8,195.68`