Discussion
A sum of ₹ 16,000 amounts to ₹ x in \(2\frac{1}{3}\) years at 15% p.a., interest compounded yearly. What is the value of x?
Answer: C
The value of x is 22,218.
For two full years compound the interest yearly; for the remaining third of a year, add simple interest at one third of the rate on the amount reached:
\[ \begin{aligned} A_2 &= 16000 \times (1.15)^{2} = 21160 \\ x &= 21160 \times \left(1 + \frac{0.15}{3}\right) \\ &= 21160 \times 1.05 = 22218 \end{aligned} \]
21,160 is the amount after only two years, before the final third of a year is added. The other figures do not follow from compounding yearly at 15% for two years and then adding interest for one third of a year.
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