Find the present value of an annuity of ₹2,000 payable at the end of each year for 3 years, if money is worth

Worked Examples · Example 3

Q. Find the present value of an annuity of ₹2,000 payable at the end of each year for 3 years, if money is worth 5% per annum compounded annually.

ChseodishaTextbookSubjectiveImportance★★★★★est

58% · 7/12 Questions

✓ Free question

Method 1 — Present-value annuity formula.

$P = 2000$ , $i = 0.05$ , $n = 3$ .

V = P\\left[\\dfrac{1-(1+i)^{-n}}{i}\\right] = 2000\\left[\\dfrac{1-(1.05)^{-3}}{0.05}\\right]

(1.05)^{-3} = \\dfrac{1}{1.157625} = 0.863838 \\;\\Rightarrow\\; \\dfrac{1-0.863838}{0.05} = \\dfrac{0.136162}{0.05} = 2.72325

V = 2000\\times2.72325 = 5446.50

✓Final answer

The present value of the annuity is ₹5,446.50 (approximately), confirmed below by discounting each payment separately.

Method 2 — Discount each payment individually (cross-check).

Year	Payment	Discount factor $(1.05)^{-t}$	Present value
1	2000	0.952381	1904.76
2	2000	0.907029	1814.06
3	2000	0.863838	1727.68
Total			5,446.50

$1904.76+1814.06+1727.68 = 5446.50$ , matching the formula — the present-value annuity factor is exactly the sum of the individual discount factors.

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2025Set ANNUAL1 markMCQ
$Q. In an ordinary annuity, payments or receipts occur at ______.$
(a) Beginning of each period
(b) End of each period
(c) Mid of each period
(d) Quarterly basis
›Reveal solutionSolution
By definition, an ordinary (immediate) annuity is one in which the equal payments or receipts occur at the end of each period; if they occurred at the beginning it would be an annuity due.

An annuity is a sequence of equal payments made at regular intervals. The classification depends on the timing of each payment within its period:

Ordinary / immediate annuity — the payment is made at the end of each period (e.g. loan EMIs, most rent-type receipts recorded at period end).

Annuity due — the payment is made at the beginning of each period.

The question refers to an ordinary annuity, so the payments or receipts occur at the end of each period. The other choices (mid of each period, quarterly basis) are not standard classifications for this definition.

✓Final answer
$Option (B) End of each period .$
CBSE 2024Set ANNUAL1 markMCQ
$Q. In an ordinary annuity, payments or receipts occur at ______.$
(a) Beginning of each period
(b) End of each period
(c) Mid of each period
(d) Quarterly basis
›Reveal solutionSolution
By definition, in an ordinary annuity each payment or receipt is made at the end of every period — option (b). (When payments are made at the beginning of each period it is called an annuity due.)

An annuity is a sequence of equal payments made at regular intervals of time. Annuities are classified by when within each period the payment occurs:

Ordinary annuity (immediate annuity): each payment is made at the end of the period.

Annuity due: each payment is made at the beginning of the period.

The question asks about an ordinary annuity, so the payments/receipts occur at the end of each period. The remaining options — beginning of each period (that is an annuity due), mid of each period, and quarterly basis (which describes only the frequency, not the timing within a period) — do not define an ordinary annuity.

✓Final answer
$In an ordinary annuity, payments or receipts occur at the end of each period — option (b) .$
CBSE 2023Set ANNUAL1 markMCQ
$Q.______ is a series of constant cash flows over a limited period of time.$
(a) Perpetuity
(b) Annuity
(c) Present value
(d) Future value
›Reveal solutionSolution
A sequence of equal payments made at equal time intervals for a fixed (limited) number of periods is an annuity; only if it continued indefinitely would it be a perpetuity. Hence option (B).

Comparing the choices:

Perpetuity — equal cash flows that continue for an unlimited (infinite) time, so it is ruled out by the word "limited period."

Annuity — a series of constant (equal) cash flows made at regular intervals for a limited, definite number of periods. This exactly matches the description.

Present value and Future value are single amounts (the discounted or accumulated worth of the flows), not the series itself.

✓Final answer
$The correct option is (B) Annuity.$

←Previous questionExample 2 — ₹1,000 is deposited at the **beginning** of each year for 3 years in a…→Next questionExample 4 — A television set has a cash price of ₹10,000. A buyer instead agrees t…

Q.Find the present value of an annuity of ₹2,000 payable at the end of each year for 3 years, if money is worth 5% per annum compounded annually.

Concept understanding — Present Value of an Annuity

Q.Find the present value of an annuity of ₹2,000 payable at the end of each year for 3 years, if money is worth 5% per annum compounded annually.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days