Q:

Find the accumulated value of an investment of $5000 for 10 years at an interest rate of 6.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously. please help

Accepted Solution

A:
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$5000\\ r=rate\to 6.5\%\to \frac{6.5}{100}\to &0.065\\ n= \begin{array}{llll} \textit{times it compounds}\\ \textit{per year} \end{array}\to &2,4,12, 365\\ t=years\to &10 \end{cases}[/tex]

[tex]\bf \stackrel{semiannually}{A=5000\left(1+\frac{0.065}{2}\right)^{2\cdot 10}}\implies A=5000(1.0325)^{20} \\\\\\ \stackrel{quarterly}{A=5000\left(1+\frac{0.065}{4}\right)^{4\cdot 10}}\implies A=5000(1.01625)^{40}[/tex]

[tex]\bf \stackrel{monthly}{A=5000\left(1+\frac{0.065}{12}\right)^{12\cdot 10}}\implies A=5000\left(\frac{2413}{2400} \right)^{120} \\\\\\ \stackrel{\textit{daily, assuming 365days per year}}{A=5000\left(1+\frac{0.065}{365}\right)^{365\cdot 10}\implies A=5000\left( \frac{73013}{73000} \right)^{3650}}[/tex]