Find the amount of each equal annual instalment needed to repay a loan of ₹1,00,000 in 5 equal yearly instalme

Worked Examples · Example 3

(1.1)^{-5} = 0.6209

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Step 1 — Recognise the loan amount as a present value. The ₹1,00,000 sanctioned today must equal the present value of the 5 future instalments, so $V=1{,}00{,}000$ , $i=0.10$ , $n=5$ .

Step 2 — Rearrange the present value formula for $P$ .

V = P\left[\dfrac{1-(1+i)^{-n}}{i}\right] \;\Rightarrow\; P = \dfrac{V\cdot i}{1-(1+i)^{-n}}

Step 3 — Substitute the known values.

$P = \dfrac{1{,}00{,}000\times0.10}{1-(1.1)^{-5}} = \dfrac{10{,}000}{1-0.6209} = \dfrac{10{,}000}{0.3791} \approx 26{,}378$ …

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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. …
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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. …
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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." …
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Q.Find the amount of each equal annual instalment needed to repay a loan of ₹1,00,000 in 5 equal yearly instalments at 10% per annum compound interest. [Given $(1.1)^{-5} = 0.6209$ ]

Concept understanding — Present Value of an Annuity

Q.Find the amount of each equal annual instalment needed to repay a loan of ₹1,00,000 in 5 equal yearly instalments at 10% per annum compound interest. [Given (1.1)−5=0.6209(1.1)^{-5} = 0.6209(1.1)−5=0.6209]

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Q.Find the amount of each equal annual instalment needed to repay a loan of ₹1,00,000 in 5 equal yearly instalments at 10% per annum compound interest. [Given $(1.1)^{-5} = 0.6209$ ]

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