Question

Each investment matures in 3 years. The interest compounds annually.

Calculate the interest and the final amount.
a) $600 invested at 5%
b) $750 invested at 4 3/4%

Answer 1

bearing in mind that 4¾ is simply 4.75.

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$600\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=600\left(1+(0.05)/(1)\right)^(1\cdot 3)\implies A=600(1.05)^3\implies A=694.575 \\\\[-0.35em] ~\dotfill`

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 4.75\%\to (4.75)/(100)\dotfill &0.0475\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=750\left(1+(0.0475)/(1)\right)^(1\cdot 3)\implies A=750(1.0475)^3\implies A\approx 862.032`

well, the interest for each is simply A - P

695.575 - 600 = 95.575.

862.032 - 750 = 112.032.