Question : A sum of Rs. 3000 becomes Rs, 4320 in 2 years at a certain rate of compound interest (compounding annually). How much this sum will become after 4 years?
Option 1: Rs. 7568.50
Option 2: Rs. 6220.80
Option 3: Rs. 6516.80
Option 4: Rs. 5128.50
Correct Answer: Rs. 6220.80
Solution :
Using the formula,
$A$ = $P(1+\frac{r}{100})^{t}$
Given that $P$ = Rs. 3000, $A$ = Rs. 4320, and $t$ = 2 years.
⇒ 4320 = 3000$(1 + \frac{r}{100})^{2}$
⇒ $(1 + \frac{r}{100})^{2}$ = $(\frac{4320}{3000})$
⇒ $(1 + \frac{r}{100})$ = $(\frac{4320}{3000})^{\frac{1}{2}}$
After 4 years, $t$ = 4
$A$ = $3000(1+\frac{r}{100})^{4}$
⇒ $A$ = $3000((\frac{4320}{3000})^{\frac{1}{2}})^{4}$
⇒ $A$ = $3000(\frac{144}{100})^{2}$
⇒ $A$ = Rs. 6220.80
Hence, the correct answer is Rs. 6220.80.
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