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nism-series-xa-sip-future-value-annuity-due-10000-monthly[ INVESTMENT ADVISER (LEVEL 1) ]

An investor invests ₹10,000 at the beginning of every month in an equity mutual fund SIP for 10 years (120 installments). Assuming an expected annualized return of 12.0% p.a., what is the accumulated Future Value (FV)?

[ A ]₹1,742,543.07
[ B ]₹3,136,577.53
[ C ]₹1,200,000
[ D ]₹2,323,390.76[ CORRECT ]
Takeaway

The SIP accumulates to ₹2,323,390.76 — because each ₹10,000 installment is invested at the start of the month, the ordinary-annuity FV formula for 120 monthly deposits must be multiplied by one extra month's growth factor (1+i).

Derivation
Step 1: Monthly rate i = 12%/12 = 1% = 0.01, n = 120 months. Step 2: FV of an ordinary annuity = 10,000 x [(1.01^120 - 1)/0.01] = ₹2,300,386.89. Step 3: Since SIPs debit at the START of each month (annuity due), multiply by (1+i): 2,300,386.89 x 1.01 = ₹2,323,390.76. This tests whether candidates remember SIPs are annuities-due, not ordinary annuities — forgetting the extra (1+i) factor is the single most common SIP FV error in the exam.
Why the others fail
A — ₹1,742,543.07
Understates the true compounded value — consistent with using a much lower effective rate or too few compounding periods than the actual 1% monthly rate over 120 months.
B — ₹3,136,577.53
Overstates growth beyond what 1% monthly compounding over 120 months can produce — consistent with double-counting the annuity-due adjustment or using an inflated rate.
C — ₹1,200,000
This is simply the sum of 120 installments of ₹10,000 with zero investment growth applied, ignoring compounding altogether.