Discussion
A sum of ₹ 8000 becomes ₹ 9500 at 7.5% p.a. in x years at simple interest. What will be the amount of the sum in same time at 20% p.a, if interest is compounded yearly ?
Answer: D
The amount is ₹ 12672.
First find the time from simple interest. The interest is 9500 - 8000 = 1500:
\[ \begin{aligned} 1500 &= \frac{8000 \times 7.5 \times x}{100} \\ 1500 &= 600x \\ x &= 2.5 \text{ years} \end{aligned} \]
At 20% compounded yearly for 2 years and then a half year at half the rate, 10%:
\[ \begin{aligned} A &= 8000 \times 1.2 \times 1.2 \times 1.1 \\ &= 11520 \times 1.1 = 12672 \end{aligned} \]
₹ 11520 would be the amount after only 2 years, and compounding for 3 full years would give ₹ 13824, which is option 1.
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