Question

To start a new business Beth deposits $1500 at the end of each six-month period in an account that pays 8%, compounded semiannually. How much will she have at the end of 9 years?

Answer 1

The amount Beth deposit every six-month is A = $1500.

The rate percent is 8% or 0.08.

The time after which futre value determined is t = 9 years.

Determine the rate percent for semi-annually.

$\begin{gathered} i=\frac{0.08}{2} \\ =0.04 \end{gathered}$

Determine the value of time (t) for semi-annualy.

$\begin{gathered} n=2\cdot9 \\ =18 \end{gathered}$

The formula for the future value is,

$FV=\frac{A}{i}\lbrack(1+i)^n-1\rbrack$

Substitute the values in the formula to determine the future value.

$\begin{gathered} FV=\frac{1500}{0.04}\lbrack(1+0.04)^{18}-1\rbrack \\ =37500\lbrack(1.04)^{18}-1\rbrack \\ =38468.11933 \\ =38468.12 \end{gathered}$

So answer is 38468.12