Question

To start a new business Beth deposits $1000 at the end of each period in an account that pays 9%, compounded monthly. How much will she have at the end of 8 years?

Answer 1

This is a future value annuity problem.

The future value annuity is given by the formula:

`\begin{gathered} FV=P*(((1+r)^n-1)/(r)) \\ \text{where P:Periodic payment} \\ r\colon\text{Rate} \\ n\colon\text{Time(years}) \end{gathered}`

From the question, we are provided with the following;

`\begin{gathered} P=\text{ \$1000} \\ r=9\text{\%} \\ n=8\text{years} \end{gathered}`

Thus, the future value annuity is:

`\begin{gathered} FV=1000*(((1+(0.09)/(12))^(8*12)-1)/((0.09)/(12))) \\ FV=1000*(((1+0.0075)^(8*12)-1)/((0.09)/(12))) \\ FV=1000*(((1.0075)^(96)-1)/(0.0075)) \\ FV=1000*((2.0489-1)/(0.0075)) \\ FV=1000*((1.0489)/(0.0075)) \\ FV=1000*139.856 \\ FV=\text{ \$139,856.16} \end{gathered}`

Hence, Beth will have $139,856.16 at the end of 8 years