A man invests ₹ 4000 for 3 years at compound interest. After one year the money amounts to ₹ 4320. What will be the amount (to the nearest rupee) due at the end of 3 years?
(a)₹ 4939
(b)₹ 5039
(c)₹ 5789
(d)₹ 6129
Answer
Answer (as printed): B
Explanation
Let the rate be R\% p.a. Then, $4000\left(1+\frac{R}{100}\right)=4320$ $$\Rightarrow 1+\frac{R}{100}=\frac{4320}{4000}=\frac{108}{100} \Rightarrow \frac{R}{100}=\frac{8}{100} \Rightarrow R=8 . \begin{aligned} \therefore \quad & \text { Amount after } 3 \text { years }=₹\left[4000\left(1+\frac{8}{100}\right)^{3}\right] \\ & =₹\left(4000 \times \frac{27}{25} \times \frac{27}{25} \times \frac{27}{25}\right)=₹\left(\frac{629856}{125}\right) \\ & =₹ 5038.848 \approx 5039 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.