Question : A sum invested at a certain rate of interest per annum, compounded annually, amounts to INR 3,600 in 2 years and to INR 6,480 in 4 years. What is the sum invested?
Option 1: INR 2,500
Option 2: INR 2,000
Option 3: INR 2,400
Option 4: INR 3,600
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Correct Answer: INR 2,000
Solution : Use: Amount = $P×(1+\frac{r}{n})^{nt}$ where, $P$ is the principal amount (the initial sum invested), $r$ is the annual interest rate (as a decimal), $n$ is the number of times interest is compounded per year, and $t$ is the time in years. For interest to be compounded annually, n = 1 After 2 years, the amount is 3,600 So, 3,600 = $P×(1+\frac{r}{1})^{1×2}$ = $P(1+r)^{2}$ After 4 years, the amount is 6,480 So, 6,480 = $P×(1+\frac{r}{1})^{1×4}$ = $P(1+r)^{4}$ Now, ⇒ $\frac{P(1+r)^{4}}{P(1+r)^{2}}$ = $\frac{6480}{3600}$ ⇒ $(1+r)^{2} = \frac{6480}{3600}$ ⇒ $(1+r)^{2} = \frac{18}{10}$ ⇒ $(1+r)^{2}$ = 1.8 So,$P$ (1 + $r$) 2 = 3,600 ⇒ $P$ × 1.8 = 3600 ⇒ $P$ = $\frac{3600}{1.8}$ ⇒ $P$ = 2000 Hence, the correct answer is INR 2,000.
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