Question

A sum of 60, 000/=was lent at simple interest and at the end of1 year and 8 months the total amount was 70, 000/=determine the rate of interest per annum​

Answer 1

we know that a year has 12 months, so 1 year plus 8 more moths will be (12+8)/12 or 20/12 years, or 5/3 year.

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$70000\\\ P=\textit{original amount deposited}\dotfill & \$60000\\ r=rate\to r\%\to (r)/(100)\\ t=years\to (20)/(12)\dotfill &(5)/(3) \end{cases} \\\\\\ 70000=60000[1+((r)/(100))((5)/(3))]\implies \cfrac{70000}{60000}=1+((r)/(100))((5)/(3))`

`\cfrac{7}{6}=1+\cfrac{5r}{300}\implies \cfrac{7}{6}=1+\cfrac{r}{60}\implies \cfrac{7}{6}-1=\cfrac{r}{60}\implies \cfrac{1}{6}=\cfrac{r}{60} \\\\\\ \cfrac{60}{6}=r\implies 10=r`