A person deposits ₹2,000 at the end of each year for 3 years into an account paying 10% per annum compounded a

Worked Examples · Example 7

Q. A person deposits ₹2,000 at the end of each year for 3 years into an account paying 10% per annum compounded annually. Find the accumulated value of this annuity. [Given (1.1)^3 = 1.331]

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Payments are made at the end of each year, so this is an immediate (ordinary) annuity with $C=2000$ , $i=0.10$ , $n=3$ :

A=C\left[\frac{(1+i)^{n}-1}{i}\right]=2000\left[\frac{(1.1)^{3}-1}{0.1}\right]=2000\left[\frac{1.331-1}{0.1}\right]=2000\times\frac{0.331}{0.1}=2000\times3.31=₹6{,}620.

Check (independent verification) — grow each deposit separately:

End of year 1 deposit earns interest for 2 years: $2000\times(1.1)^{2}=2000\times1.21=₹2{,}420$ . …

Q.A person deposits ₹2,000 at the end of each year for 3 years into an account paying 10% per annum compounded annually. Find the accumulated value of this annuity. [Given (1.1)^3 = 1.331]