Question

R120 000 is deposited into a savings account and two years later a further deposit of R6 000 is added to the savings. Calculate the amount of money in the savings account at the end of 6 years if the interest rate is 8% p.a

. compounded monthly.
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Answer 1

let's first check how much is it for R120,000 for the first two years.

`~~~~~~ \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 &\$120000\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &2 \end{cases}`

`A = 120000\left(1+(0.08)/(12)\right)^(12\cdot 2) \implies A = 120000( 1.00\overline{66})^(24)\implies A \approx 140746.55`

now, two years later we'll add the R6000 to that amount in the account and let's see what it'd be after 4 years.

`~~~~~~ \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 &\$\stackrel{ 140746.55+6000 }{146746.55}\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases}`

`A \approx 146746.55\left(1+(0.08)/(12)\right)^(12\cdot 4) \\\\\\ A \approx 146746.55( 1.00\overline{66})^(48)\implies \boxed{A \approx 201874.25}`