Question

Amit lent out Rs. 900 on the condition that the loan is payable in 10 months in 10 equal instalments of Rs. 100 each. Find the rate of interest per annum.

• A. $25$
• B. $frac2623\%$
• C. $frac2313\%$
• D. $28\%$

Answer 1

Is similar to recurring deposit scheme of bank
Let the interest per annum be r% per annum. Hence it is $r/12\%$ per month.
The first instalement of Rs 100 earns interest for 10 months
$\frac{r}{1200}\times 100\times 10=\frac{r}{12}\times 10$
The second instalment of Rs 100 earns interest for 9 months = $\frac{r}{12}\times 9$
The third instalment of Rs 100 earns interest for 8 months =$\frac{r}{12}\times \mathrm{8......}andsoonuptothelastmonth.Hence,thetotalinterestearned=\frac{r}{12}(1+2+3+4\dots 10)=\frac{r}{12}\times 55$.
However, the actual interest = 1000 (10 instalment of Rs 100 each) - Rs 900 (principal) = Rs 100
Therefore, $\frac{r}{12}\times 55=100\to r=\frac{1200}{55}=21.81\%$.
None of the options have this figure. Hence, it is felt that the options are not proper.