Question : A sum of Rs. 7500 amounts to Rs. 15000 in two years at compound interest calculated annually. How much will Rs. 7500 becomes in four years?
Option 1: Rs. 60000
Option 2: Rs. 30000
Option 3: Rs. 50000
Option 4: Rs. 45000
Correct Answer: Rs. 30000
Solution :
Amount = $P \times (1 + \frac{R}{100})^T$
where $P$ = Principal or the initial amount, $R$ = rate of interest and $T$ = time.
⇒ $15000 = 7500 \times (1 + \frac{r}{100})^2$
⇒ $2 = (1 + \frac{r}{100})^2$
⇒ $[(1 + \frac{r}{100})^2]^2=(2)^2$ [Squaring both sides]
⇒ $(1 + \frac{r}{100})^4=4$
⇒ $7500(1 + \frac{r}{100})^4=4×7500$ [Multiplying both sides with 7500]
⇒ $7500(1 + \frac{r}{100})^4=30000$
So, in 4 years Rs. 7500 will become Rs. 30000.
Hence, the correct answer is Rs. 30000.
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