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
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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