Question

$618 for 51⁄2 years at 101⁄2% compoundedsemi-annually. Find the accumulated amount.

Answer 1

Given: Principal amount of P= $618 compounded semi-annually for

$\begin{gathered} t=5\frac{1}{2}\text{ years at} \\ r=10\frac{1}{2}\% \\ \end{gathered}$

Required: To find the accumulated amount.

Explanation: The amount after t years at a rate of r% compounded semi-annually is

$A=P(1+\frac{r}{2})^{2t}$

Here,

$\begin{gathered} r=10\frac{1}{2}\% \\ =0.105 \\ \\ t=5\frac{1}{2} \\ =\frac{11}{2}\text{ years} \\ P=618\text{ \ } \end{gathered}$

Putting these values gives

$A=618(1+\frac{0.105}{2})^{11}$

Solving this gives the value

$A=1085\text{ \ }$

Final Answer: The accumulated amount is $1085.