Question

After 10 years, the investment compounded periodically will be worth XXXX more than the investment compounded annually.

Answer 1

Given:

`P=\text{ \$3000 ; interest rate(r)=}9\text{ \%= 0.09 ; t=10 years}`

Amount compounded annually, n=1

`A=P(1+(r)/(n))^(nt)`
`\begin{gathered} A=3000(1+0.09)^(10) \\ A=3000(1.09)^(10) \\ A=7102.09 \\ A=\text{ \$7102.09} \end{gathered}`

Amount compounded 2 periods in a year, n=2

`\begin{gathered} A=3000(1+(0.09)/(2))^(20) \\ A=3000((2.09)/(2))^(20) \\ A=\text{ \$7235.14} \end{gathered}`
`\begin{gathered} \text{Difference amount=7235.14-7102.09} \\ \text{Difference amount= \$133.05} \end{gathered}`