M00 · Problem 4 ★★ Check

Step-up SIP

A SIP starts at ₹10,000 a month and is raised by 10% at the start of each year (so ₹11,000 a month in year 2, and so on) for 10 years. The fund earns 12% a year. (a) Show that the value after 10 years is

FV = P\,A\,\frac{(1+r)^Y - (1+s)^Y}{r - s}, \qquad A = (1+i)\frac{(1+i)^{12} - 1}{i},

with $P = 10{,}000$ , $s = 0.10$ , $r = 0.12$ , $Y = 10$ and $(1+i)^{12} = 1+r$ . (b) Evaluate it, and compare with the total invested and with a flat ₹10,000 SIP.

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