Find the sum of money which will amount to Rs.10,404 in 6 months at the rate of 8 per cent per anum when the
interest is compounded quarterly.

Correct option is A

Given:
Final amount A=10,404
Time t=6 months=0.5 year
Rate of interest R=8% per annum
Interest is compounded quarterly, so:
Quarterly rate = $$\frac{8}{4} = 2\%$$​
Number of quarters = $$0.5×4=\text{2quarters} .\frac{8}{4} = 2\%$$​ ​​
The compound interest formula is:
​$$A= P \left( 1 + \frac{R}{100} \right)^nA=P\left(1+100R) \right)^n$$​​
Where:
A = final amount
P = principal
R = interest rate per quarter
n = number of quarters
Substitute the values into the formula:
$$10,404= P \left( 1 + \frac{2}{100} \right)^210,404= P \left( 1.02 \right)^210,404=P\left(1.02\right)^2$$​

Solve for P:
$$P= \frac{10,404}{1.0404}$$​

P=10,000