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
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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