The compound interest on a sum of ₹8,000 becomes ₹1,261 in 18 months. Find the rate of interest if interest is compounded half-yearly.

Correct option is C

Given:

Principle = ₹8000

Interest = ₹1261

Time =18 months

Formula Used:

Compounded Amount =$$Principle \times (1+ \frac{r}{100})^{t}$$​​

Amount = Principle + Interest

Solution:

Here interest is calculated half yearly hence time =$$\frac{18}{6} = 3 \ half-years$$​​

Amount = 8000 + 1261 = ₹9261

​$$9261 = 8000 (1+ \frac{r}{100})^{3}$$​​

​$$(\frac{9261}{8000}) = (1+ \frac{r}{100})^{3}$$​​

​$$(\frac{21}{20})^3 = (1+ \frac{r}{100})^{3}$$​​

​$$\frac{21}{20} =1+ \frac{r}{100}$$​​

​$$\frac{21}{20} -1 = \frac{r}{100}$$​​

​$$\frac{1}{20} = \frac{r}{100}$$​​

​$$r= \frac{100}{20} =5\%$$​​

This rate is half yearly rate;

Rate of interest per annum = $$2 \times 5 = 10\%$$​​