Question

Find the ordindary interest on a loan of $2780 at 7% annually for 316 days

Answer 1

well, let's assume a year has 365 days, that means 316 days is really just 316/365 of a year, so

`~~~~~~ \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 &\$2780\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\to \dotfill &(316)/(365) \end{cases}`

`A=2780\left(1+(0.07)/(1)\right)^{1\cdot (316)/(365)} \implies A = 2780(1.07)^{(316)/(365)}\implies A\approx 2947.70 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \underset{earned~interest}{\stackrel{2947.70~~ - ~~2780}{\approx\text{\LARGE 167.7}}}~\hfill`