NISM Series X-A · Chapter 2: Time Value of Money

L1 · Foundation

Foundation — Why money has time value, and present and future value

The two reasons a rupee today beats a rupee tomorrow, the four rules that follow, the four parameters of every TVM problem, and the present value and future value formulae with the chapter worked examples including simple versus annual versus quarterly compounding.

14 min read · Worth 6% of the paper · Written from pages 31–43 of the official NISM workbook · Updated 18 September 2026

2.1 The time value of money

"The value of money DOES NOT REMAIN THE SAME at all points of time. The money available at the PRESENT time is WORTH MORE than the same amount in the future SINCE IT HAS THE POTENTIAL TO EARN RETURNS (or interest as the case may be)."

The chapter's opening choice, "assuming there is no uncertainty associated with the cash flow":

Receiving Rs 100 now
Receiving Rs 100 after one month

"ALL investors would PREFER TO RECEIVE THE CASH FLOW NOW, rather than wait for a month, though the amount to be received has the same value." Two reasons:

"INSTINCTIVE PREFERENCE FOR CURRENT CONSUMPTION OVER FUTURE CONSUMPTION"
"ABILITY TO INVEST the Rs 100 for a month like a BANK ACCOUNT OR DEPOSIT and EARN A RETURN so that it GROWS IN VALUE to MORE THAN Rs 100 after one month"

"The time value of money received in EARLIER periods as compared to that received in later time periods will be HIGHER. Since most decisions in finance involve cash flows SPREAD OVER MORE THAN ONE PERIOD (monthly, quarterly, yearly etc.) the time value of money is a KEY PRINCIPLE IN FINANCIAL DECISION-MAKING."

The historical note

"Records dating as far back as 5000 BC indicate that the MESOPOTAMIANS, HITTITES, PHOENICIANS, and EGYPTIANS CHARGED INTEREST when they loaned such items as OLIVES, DATES, SEEDS, AND ANIMALS. The time value of any loaned item was perhaps EASIEST TO SEE WITH THE LOANING OF SEEDS because any successfully planted seed would yield a plant that would PRODUCE MORE ADDITIONAL SEEDS."

The compensation calculation

"suppose the Rs 100 received now is placed in a ONE-MONTH BANK DEPOSIT YIELDING 6 per cent p.a. After a month, the value would grow to Rs 100.50. If an investor has to opt for receiving Rs 100 after a month, then he needs to be COMPENSATED BY Rs 0.50, the amount that has been FOREGONE by waiting for a month. The two options will be EQUIVALENT from the investor's point of view if the option is to receive Rs 100 NOW or Rs 100.50 AFTER ONE MONTH."

The four points to note

Point	The chapter's words
Discounting	"FUTURE inflows are DISCOUNTED by a relevant rate to reach their PRESENT VALUE; this rate is known as the DISCOUNT RATE or RETURN RATE or INTEREST RATE"
Compounding	"PRESENT inflows are INCREASED at a relevant rate to reach their FUTURE VALUES; this rate is known as the COMPOUND INTEREST RATE"
Time	"The LATER in the future a cash flow is likely to be received, the LOWER its value at the current time. Rs 100 available after one month is more valuable today than Rs 100 available after one year, which has a better value today than Rs 100 available after 5 years"
Rate	"The HIGHER the discount rate, the LOWER the present value of future cash flows. A higher rate means that investors have to FOREGO MORE RETURNS by opting to receive the money today"

The chapter's own illustration of the rate effect: "Rs 1,000 received after 3 years when discounted at 5 per cent is worth Rs 864 today but the same amount discounted at 8 per cent is worth ONLY Rs 794."

The four parameters of every TVM problem

a. Cash inflows or outflows — "could be either in the form of SINGLE PERIOD cash flow or in the form of an ANNUITY or a STREAM OF UNEVEN OR EVEN CASH FLOWS"
b. Rate of interest — "Also known as COMPOUNDING RATE or DISCOUNT RATE or REINVESTMENT RATE"
c. Time period — "may be ANNUAL or ANY OTHER FRACTION thereof like monthly, quarterly etc."
d. Frequency of cash flows — "which may or may not be FIXED"

"Financial problems involving time value of money are usually concerned with CALCULATING ONE OF THE ABOVE PARAMETERS."

2.2.1 Present value

"Present value is the amount that you would PAY TODAY for a cash flow that COMES IN THE FUTURE. It BRINGS THE FUTURE VALUE DOWN TO TODAY'S PRICE."

"There are TWO WAYS in which the present value can be calculated."

Single future amount

"For a ONE TIME RECEIPT, PV is calculated as per the following formula: PV = C ÷ (1 + r)^n"

The chapter's example: "there can be a future payment of Rs 50,000 that might be received after a period of 5 years earning 6 per cent."

PV = 50,000 ÷ (1.06)^5 = Rs 37,362.91

A regular cash flow

The chapter's example: "Shyam is going to receive a sum of Rs 6,500 a year for the next 8 years at an interest rate of 7 per cent. He would like to know whether he should take the cash flow or a lump sum now."

Discounting each year separately:

PV = 6500/(1.07)^1 + 6500/(1.07)^2 + 6500/(1.07)^3 + 6500/(1.07)^4 + 6500/(1.07)^5 + 6500/(1.07)^6 + 6500/(1.07)^7 + 6500/(1.07)^8 = 38,813.44

Or by formula: PV = 6500 × [(1 − (1 ÷ (1.07)^8)) ÷ 0.07] — the same Rs 38,813.44.

"In the excel function the rate of return has to be put in as 0.07, the nper as 8 and the payment figure (pmt) as −6500."

"In this sum, type is to be put as 0, assuming the cash flows are at the END of the year."

2.2.2 Future value

"Future value represents what something is worth at SOME POINT IN THE FUTURE."

"Note that the rate of return for each compounding period HAS TO BE ADJUSTED FOR THE FREQUENCY OF COMPOUNDING. For example, if an investment pays 8% interest p.a. compounded QUARTERLY, then the applicable rate of return for each compounding period is 8%/4, or 2%."

"The number of compounding periods (n) refers to the PERIODICITY WITH WHICH INTEREST IS PAID on the investment during the year. For example, the POST OFFICE MONTHLY INCOME SCHEME (MIS) pays interest EVERY MONTH, while the SENIOR CITIZENS SCHEME pays EVERY QUARTER. The GREATER the frequency of compounding, the MORE OFTEN interest is paid ON INTEREST, and the GREATER are returns earned through compounding."

The Krishna example — three scenarios

"Krishna invests Rs 5 lakhs in a 5 year bank deposit that pays 8% interest compounded annually."

Scenario 1 — "the interest is used to pay the COLLEGE FEES of his daughter and there is NO COMPOUNDING."

Interest = Rs 5,00,000 × 8% × 5 = Rs 2,00,000

"There is NO COMPOUNDING BENEFIT since the interest is TAKEN OUT AND USED and NOT RE-INVESTED. This is also known as the SIMPLE INTEREST."

Scenario 2 — "the CUMULATIVE option is chosen and the interest is paid at maturity i.e. interest is compounded YEARLY."

Maturity value = 5,00,000 × (1 + 8%)^5 = Rs 7,34,664 Interest = 7,34,664 − 5,00,000 = Rs 2,34,664

"The interest income is HIGHER because the interest earned each year is RE-INVESTED AND EARNS INTEREST TOO. This is the COMPOUNDING BENEFIT."

Scenario 3 — "the interest is instead compounded QUARTERLY and he chooses the cumulative option."

"the rate [is] divided by 4 while the total quarterly periods are 20 during the 5 years"

Maturity value = 5,00,000 × (1 + 2%)^20 = Rs 7,42,974 Interest = 7,42,974 − 5,00,000 = Rs 2,42,974

"The interest income is HIGHER THAN SCENARIO 2 because the FREQUENCY OF COMPOUNDING IS HIGHER. The interest is paid each quarter and this earns interest for the remaining period."

Scenario	Method	Maturity	Interest over 5 years
1	Simple interest, paid out	Rs 5,00,000 returned	Rs 2,00,000
2	Annual compounding, cumulative	Rs 7,34,664	Rs 2,34,664
3	Quarterly compounding, cumulative	Rs 7,42,974	Rs 2,42,974

"a sum of Rs 5,000 growing at 8 per cent per annum will become Rs 7,346.64 in 5 years — FV(0.08, 5, , −5000, , 0)."

Think of it like this

Seeds in the ground, 5000 BC

The chapter reaches back seven thousand years for the clearest possible illustration. The Mesopotamians and Egyptians "charged interest when they loaned such items as OLIVES, DATES, SEEDS, AND ANIMALS", and "the time value of any loaned item was perhaps EASIEST TO SEE WITH THE LOANING OF SEEDS because ANY SUCCESSFULLY PLANTED SEED WOULD YIELD A PLANT THAT WOULD PRODUCE MORE ADDITIONAL SEEDS." A sack of seeds today is not the same as a sack next season — this season's sack can be planted. Money is the same sack in a different form.

Rs 100 today equals Rs 100.50 in a month, not Rs 100

The chapter converts the abstraction into an exact number. Put Rs 100 in a one-month deposit at 6 per cent p.a. and it becomes Rs 100.50. So if you are asked to wait a month, "he needs to be COMPENSATED BY Rs 0.50, the amount that has been FOREGONE by waiting." The two offers become equivalent at Rs 100 now versus Rs 100.50 later. Every present value calculation in this chapter is just this sentence run backwards.

The higher the discount rate, the harsher the haircut

Two numbers from the chapter make the rate effect concrete: Rs 1,000 received after 3 years is worth Rs 864 today at 5 per cent, but only Rs 794 at 8 per cent. The same future rupee shrinks more when money can earn more elsewhere — because "a higher rate means that investors have to FOREGO MORE RETURNS by opting to receive the money today." Waiting is expensive in a high-rate world and cheap in a low-rate one.

Rs 2,00,000, Rs 2,34,664, Rs 2,42,974 — same deposit, three answers

Krishna invests the same Rs 5 lakh at the same 8 per cent for the same 5 years three times over, and earns three different amounts. Taking the interest out each year gives simple interest of Rs 2,00,000. Letting it compound annually gives Rs 2,34,664. Compounding it quarterly gives Rs 2,42,974. Nothing changed except whether the interest was reinvested and how often. That Rs 42,974 gap is what the chapter means by "the compounding benefit."

Frequency: MIS pays monthly, Senior Citizens Scheme pays quarterly

The chapter grounds compounding frequency in two schemes every Indian adviser knows: "the POST OFFICE MONTHLY INCOME SCHEME (MIS) pays interest EVERY MONTH, while the SENIOR CITIZENS SCHEME pays EVERY QUARTER." And the rule that follows: "The GREATER the frequency of compounding, the MORE OFTEN interest is paid ON INTEREST, and the GREATER are returns." But note the catch built into MIS — if the monthly interest is spent rather than reinvested, the frequency advantage disappears entirely, exactly as in Krishna's Scenario 1.

Adjust the rate AND the periods — both, together

The single most common arithmetic slip in this chapter. For quarterly compounding at 8 per cent over 5 years, the rate becomes "8%/4, or 2%" and the periods become "20 during the 5 years." Change one without the other and the answer is badly wrong: 8 per cent over 20 periods, or 2 per cent over 5. The same discipline applies to the EMI example later — 6.5 per cent becomes 0.065/12, and 20 years becomes 240 months.

Two roads to Rs 38,813.44

Shyam's eight annual receipts of Rs 6,500 at 7 per cent can be valued by discounting each of the eight separately and adding them up, or by the single annuity formula C × [(1 − (1 ÷ (1+r)^n)) ÷ r]. The chapter shows both and both give Rs 38,813.44. The long way explains why; the short way is what you use under exam time pressure. Knowing they are the same calculation is what stops the formula being something you merely memorise.

Present value is a price, not a prediction

The chapter's definition is worth reading as commercial advice rather than mathematics: "Present value is THE AMOUNT THAT YOU WOULD PAY TODAY for a cash flow that comes in the future." When Shyam is offered a lump sum instead of eight yearly payments of Rs 6,500, PV answers exactly one question — is the lump sum more or less than Rs 38,813? That is the form almost every real advisory question takes: a stream on one side, a single number on the other, and PV as the only honest way to compare them.

Key terms in this chapter

Annuity: A sum of money paid at regular periods such as monthly, quarterly or annually. Pension is the common example, and annuities are used extensively during retirement.
Annuity due: An annuity where payment is made at the START of the period, which raises its value. Excel type is 1. More valuable to the receiver and more costly to the payer.
Annuity table: A table giving a multiple, or annuity factor, for different rates and time periods, which can be multiplied by the cash flow.
CAGR: Compounded annual growth rate: the underlying compound interest rate that equates the end value of an investment with its beginning value. The accepted standard measure of return, except for periods of less than one year.
Compounding benefit: The extra return that arises because interest earned each period is reinvested and itself earns interest.
Compounding period: The periodicity with which interest is paid on the investment during the year. The rate must be divided by, and the periods multiplied by, the frequency.
Compound interest rate: The rate at which present inflows are increased to reach their future value.
Discount rate: The rate at which future inflows are discounted to reach their present value. Also called the return rate or interest rate.
EMI: Equated Monthly Instalment, the regular payment made to a lender. Computed in Excel with the PMT function using the monthly rate and the number of months.
Fixed annuity: An annuity where fixed returns are received at regular periods, such as a bank fixed deposit paying 5.5 per cent for a predetermined assured term.
Floating annuity: An annuity whose returns are benchmarked to inflation, index returns or another benchmark specified in the indenture agreement, so payments change with the benchmark.
Fractional period CAGR: For holdings not in whole years, convert days to years and use the reciprocal as the exponent.
Frequency of compounding: How often interest is credited. The greater the frequency, the more often interest is paid on interest and the greater the returns. Post Office MIS pays monthly; the Senior Citizens Scheme pays quarterly.
Future value (FV): What something is worth at some point in the future, computed as PV times (1 + r) to the power n.
NPER function: The Excel function returning the number of periods needed to repay a loan, given the rate, the equal payment and the present value.
Ordinary annuity: An annuity where payment is made at the END of the relevant period. Most annuities are of this type, such as a bond paying annually. Excel type is 0 or blank.
Perpetual bond: The best real-life example of a perpetuity: a bond on which the cash flow keeps coming year after year with no maturity.
Perpetuity: A cash flow from an investment that goes on forever, with no finite period. Its present value is the cash flow divided by the discount rate.
PMT function: The Excel function returning the periodic payment, taking the rate, the number of periods and the present value of the loan.
Present value (PV): The amount you would pay today for a cash flow that comes in the future. It brings the future value down to today's price.
Simple interest: Interest computed only on the principal because the interest is taken out and used rather than reinvested, so there is no compounding benefit.
Time value of money (TVM): The value associated with the same sum of money received at various points on the timeline. Money received earlier is worth more than the same amount received later.

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Original explanatory writing based on the official NISM workbook for Series X-A, which is published and copyrighted by NISM. Check figures against the current edition at nism.ac.in.

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