Question

Find the compound interest and the total amount after 1 year and 1 month if the interest is compounded

quarterly.
Principal = £768
Rate of interest - 100% per annum
Total amount = £
Compound interest = £

Answer 1

well, there are 12 months in a year, so, for a year and 1 month that'll be 13 months, or namely 13/12 ths of a 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 &\pounds768\\ r=rate\to 100\%\to (100)/(100)\dotfill &1.00\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &(13)/(12) \end{cases}`

`A=768\left(1+(1.00)/(4)\right)^{4\cdot (13)/(12)}\implies A=768(1.25)^{(13)/(3)}\implies A\approx \stackrel{\pounds}{2019.78} \\\\\\ \stackrel{~\hfill \textit{interest yielded}}{2019.78~~ - ~~768~~ \approx ~~ \stackrel{\pounds}{1251.78}}`