Question

Please explain me question no 18 with standard of class 9

Answer 1

10%

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
`(x)/(2)` %.

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

`S = P(1 + (r)/(100) )^(n)`

where S = Sum, P = Principal, r = rate of interest for the interval of compounding, and n = number of times of compounding.

So,
`48620.25 = 40000(1 + (x)/(2 * 100) )^(4)`

⇒
`(1 + (x)/(2 * 100) ) = 1.05`

⇒
`(x)/(2 * 100) = 0.05 = (1)/(20)`

⇒ x = 10%.

Therefore, the rate of interest per annum is 10%. (Answer)