Question

Felicia invests a sum of money into a savings account which gets 4.25% per year compound interest.

After 25 years Felicia has £10380 in the account.

How much did Felicia invest in the account at the beginning?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 10380\\ P=\textit{original amount deposited}\\ r=rate\to 4.25\%\to (4.25)/(100)\dotfill &0.0425\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &25 \end{cases}`

`10380 = P\left(1+(0.0425)/(1)\right)^(1\cdot 25) \implies 10380=P(1.0425)^(25) \\\\\\ \cfrac{10380}{(1.0425)^(25)}=P\implies 3666.87\approx P`