Question

Miss Diale managed to save R20 000 and decided to invest it for two years compounded annually,at an interest rate of 7,73% for the first year and 7,98% for second year

Calculate the total amount she will receive at the end of the investment period.

Answer 1

well, let's check the amounts after the first year and second year.

`~~~~~~ \stackrel{ \textit{\LARGE first year} }{\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 &\$20000\\ r=rate\to 7.73\%\to (7.73)/(100)\dotfill &0.0773\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}`

`A = 20000\left(1+(0.0773)/(1)\right)^(1\cdot 1) \implies A = 20000( 1.0773)\implies \boxed{A = 21546} \\\\[-0.35em] ~\dotfill`

`~~~~~~ \stackrel{ \textit{\LARGE second year} }{\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 &\$21546\\ r=rate\to 7.98\%\to (7.98)/(100)\dotfill &0.0798\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}`

`A = 21546\left(1+(0.0798)/(1)\right)^(1\cdot 1) \implies A = 21546( 1.0798) \\\\\\ ~\hfill~ {\Large \begin{array}{llll} A \approx 23265.37 \end{array}}~\hfill`