Discussion
A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?
Answer: C
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Each year's saving is lent as it is made, so by the end of the third year the three deposits have been earning for 3, 2 and 1 years respectively.
\[ A = 200(1.05)^{3} + 200(1.05)^{2} + 200(1.05) \]
\[ = 200(1.157625) + 200(1.1025) + 200(1.05) \]
\[ = 231.53 + 220.50 + 210.00 = \text{Rs. } 662.02 \]
The deposits cannot be pooled and compounded together, because each has been invested for a different length of time - treating all Rs. 600 as present from the start would give Rs. 694.58.
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