$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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This is an annuity.$3000 is invested yearly at 9% pa which is paid each half-year.
Find amount of the investment after 18 years.
Formula: .$\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 $\displaystyle \$258,\!491.90$