$3000 is invest yearly at 9%pa which is paid each half year, for 18yrs. Find the amount of the investment after 18yrs

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- Jul 8th 2009, 03:45 AMnerdzorSuperannuation
$3000 is invest yearly at 9%pa which is paid each half year, for 18yrs. Find the amount of the investment after 18yrs

- Jul 8th 2009, 02:05 PMpickslides
$\displaystyle A = P \left(1+\frac{r}{100}\right)^n$

where $\displaystyle P= 3000, r = 9$ & $\displaystyle n = 18$

$\displaystyle A = 3000 \left(1+\frac{9}{100}\right)^{18}= \dots$ - Jul 8th 2009, 03:07 PMSoroban
Hello, nerdzor!

Quote:

$3000 is invested yearly at 9% pa which is paid each half-year.

Find amount of the investment after 18 years.

.*annuity*

Formula: .$\displaystyle A \:=\:D\!\cdot\!\frac{(1+i)^n-1}{i}$

. . where: .$\displaystyle \begin{Bmatrix}D &=& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \\ A &=& \text{final amount} \end{Bmatrix}$

We have: .$\displaystyle D \:=\:3000 \qquad i \:=\:\frac{9\%}{2} \:=\:0.045 \qquad n \:=\: 36 $

Hence: .$\displaystyle A \;=\;3000\!\cdot\!\frac{1.045^{36}-1}{0.045} \;=\;258491.8974 $

The investment will be worth $\displaystyle \$258,\!491.90$