Answer:
10%
Step-by-step explanation:
If Rs. 40000 amounts to Rs. 48620.25 in 2 years, and the interest compounded half-yearly, then we have to find the rate of interest per annum.
Let the principal is getting an x% interest rate per annum.
Therefore, half-yearly interest rate is [tex]\frac{x}{2}[/tex] %.
Again, the interest will be compounded for (2 × 2) = 4 times within the period of 2 years.
Therefore, from the formula of compound interest, we have
[tex]S = P(1 + \frac{r}{100} )^{n}[/tex]
where S = Sum, P = Principal, r = rate of interest for the interval of compounding, and n = number of times of compounding.
So, [tex]48620.25 = 40000(1 + \frac{x}{2 \times 100} )^{4}[/tex]
⇒ [tex](1 + \frac{x}{2 \times 100} ) = 1.05[/tex]
⇒ [tex]\frac{x}{2 \times 100} = 0.05 = \frac{1}{20}[/tex]
⇒ x = 10%.
Therefore, the rate of interest per annum is 10%. (Answer)
