An amount becomes ₹40,84,101 at 20% per annum for 15 months, which is compounded quarterly. What was the principal?

Correct option is C

Given:

Rate of interest = 20%

Time = 15 months

Amount = ₹40,84,101

Formula Used:

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

Solution:

Interest is compounded quarterly so here t = $$\frac{15}{3} = 5$$​

Rate of interest becomes =$$\frac{20}{4} = 5\%$$​​

​$$40,84,101 =P \times \left(1+ \frac{5}{100}\right)^{5}$$​​

​$$40,84,101 =P \times \left( \frac{105}{100}\right)^{5}$$​​

​$$40,84,101 =P \times \left( \frac{21}{20}\right)^{5}$$​​

​$$40,84,101\times \left(\frac{20}{21}\right)^{5} =P$$​

​$$P = ₹32,00,000$$​​