Question : If a sum of money amounts to Rs. 12,900 and Rs. 14,250 at the end of the 4th year and 5th year, respectively at a certain rate of simple interest, then the rate of interest is:
Option 1: 10%
Option 2: 12%
Option 3: 18%
Option 4: 20%
Correct Answer: 18%
Solution :
Total amount at the end of 5th year = Rs. 14,250
Total amount at the end of 4th year = Rs. 12,900
Let $R$ be the rate.
Simple Interest in one year
= Total amount at the end of 5th year – Total amount at the end of 4th year
= 14250 – 12900
= 1350
$\therefore$ Simple interest at the end of 4th year = 1350 × 4 = Rs. 5,400
Sum, $P$ = Total amount – Simple interest = 12,900 – 5400 = Rs. 7,500
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
$⇒ 5400 = \frac{7500×4×R}{100}$
$\therefore R= 18\%$
Hence, the correct answer is 18%.
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