Question : An amount of money appreciates to Rs. 7,000 after 4 years and to Rs. 10,000 after 8 years at a certain compound interest annually. The initial amount of money was:
Option 1: Rs. 4,700
Option 2: Rs. 4,900
Option 3: Rs. 4,100
Option 4: Rs. 4,300
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Correct Answer: Rs. 4,900
Solution : Given: An amount of money appreciates to Rs. 7000 after 4 years and to Rs. 10000 after 8 years. When compounded annually, $ A= P(1+\frac{R}{100})^{T}$, where $A$ is the total amount, $P$ is the principal amount, $R$ is the rate of interest per annum, and $T$ is the time in years. So, $7000= P(1+\frac{R}{100})^{4}$ ------------------(i) ⇒ $10000= P(1+\frac{R}{100})^{8}$ -----------------(ii) On dividing (ii) by (i) we get, ⇒ $(1+\frac{R}{100})^{4} = \frac{10}{7}$ Now substituting this value in equation (i), we get, ⇒ $P \times (1+\frac{R}{100})^{4} = 7000$ ⇒ $P \times \frac{10}{7} = 7000$ $\therefore P = 4900$ Hence, the correct answer is Rs. 4,900.
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