The amount of ₹ 900 becomes ₹ 1600 in 10 yr at compound interest. At the same interest rate will be ₹ 9000 in half the time, so that the amount is

Correct option is A

Given:

Principal (P₁) = ₹900

Amount (A₁) = ₹1600

Time (T₁) = 10 years

Required: Find the amount when ₹9000 is invested for 5 years (half the time) at the same compound interest rate.

Formula Used:

First, find the compound interest rate using the formula:

​$$A = P(1 + \frac r{100})^t$$​​

Solution:

​$$\frac{A_1}{P_1} = (1 + r)^{t_1} \\ \ \\ \frac{1600}{900} = (1 + r)^{10}$$​​

​$$\frac{16}{9} = (1 + r)^{10}$$​​

1 + r = $$\left(\frac{16}{9}\right)^{1/10}$$​​

Now:

Amount when P₂ = ₹9000, T₂ = 5 years

​$$A_2 = 9000 \times \left(\left(\frac{16}{9}\right)^{1/10}\right)^5 \\ \ \\ = 9000 \times \left(\frac{16}{9}\right)^{1/2}$$​​

​$$= 9000 \times \frac{4}{3} = 12000$$​​