Question

Beth took out a loan at an annual compound interest rate of 30%.After 2 years she owes a total of £8112.What was the original amount that Beth Borrowed.Give your answer to the nearest £1

Answer 1

now, we don't have a compounding period above, so we're assuming the amount is compounding annually.

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\pounds 8112\\ P=\textit{original amount deposited}\\ r=rate\to 30\%\to (30)/(100)\dotfill &0.30\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}`

`8112=P\left(1+(0.30)/(1)\right)^(1\cdot 2)\implies 8112=P(1.3)^2\implies \cfrac{8112}{1.3^2}=P\implies 4800=P`