Question

$7000 is compounded semiannually at a rate of 11% for 21years Find the total amount and round to the nearest cent

Answer 1

$\text{Given that }\ 7000 \text{ is compounded semiannualy at a rate of }11\% \text{ for 21 years}\\ \\ \text{we know that the amount after t year when compounded is given by}\\ \\ A=P\left ( 1+\frac{r}{n} \right )^{nt}\\ \\ \text{here P is the principal amoount, so }P=7000,\\ \\ \text{r is the interest rate, }r=11\%=0.11\\ \\ \text{n is the number of times in a year, here semiannulay, so }n=2,\\ \\ \text{and t is the time, so }t=21\\ \\ \text{so the amount after 21 years is}$

$A=7000\left ( 1+\frac{0.11}{2} \right )^{2(21)}\\ \\ \Rightarrow A=7000\left ( 1+0.055 \right )^{42}\\ \\ \Rightarrow A=7000\left ( 1.055 \right )^{42}\\ \\ \Rightarrow A\approx 66328.68$

So the amount after 21 years is: $66328.68