Question

Alfred invests some money into an account that pays 0.75% compound interest per annum. work out after how many years Alfred will have trebled the investment?

Answer 1

let's give Alfred say an original amount of 1 buck, so the issue will be, how long before that $1 becomes $3?

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\ 3\\ P=\textit{original amount deposited}\dotfill &\ 1\\ r=rate\to 0.75\%\to \frac{0.75}{100}\dotfill &0.0075\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &t \end{cases}$

$3=1\left(1+\frac{0.0075}{1}\right)^{1\cdot t}\implies 3=1.0075^t\implies \log(3)=\log\left( 1.0075^t \right) \\\\\\ \log(3)=t\log\left( 1.0075 \right)\implies \cfrac{\log(3)}{\log(1.0075)}=t\implies 147\approx t$

by the time that triples, we'll be driving flying saucers.