Time value of money
Also written TVM · Present value of money · Value of money over time
The principle that the same sum of money is worth different amounts at different points on a timeline, because money held today can be invested and because inflation erodes what it will buy.
In plain language
Rs 100 today and Rs 100 a year from now are not the same thing, and a retirement plan that treats them as the same is wrong before it starts.
Two separate forces pull in opposite directions. The rupee in your hand can be invested, so it grows. The rupee arriving next year buys less, because prices have risen in the meantime. The workbook puts both in one paragraph: at 8 percent, Rs 100 today is Rs 108 in a year; at 6 percent inflation, what costs Rs 100 today costs Rs 106 in a year.
Every number in a retirement plan — the expense figure, the corpus, the monthly saving — has to be stamped with the date it belongs to.
How it works
The workbook identifies three places where time value bites in a retirement calculation:
- Expenses expected in retirement must be inflated. The same standard of living costs more later, so the corpus must be larger.
- Savings will earn returns and compound. The final corpus is contributions plus returns, and the returns do most of the work — which is what reduces the monthly saving required.
- The longer the runway, the larger both effects. Time amplifies compounding and inflation together.
The direction of travel tells you which operation to use. Moving a number forward in time is compounding; moving it backward is discounting. They are the same equation read in opposite directions.
The formula
Future value: FV = PV × (1 + r)^n
Present value: PV = FV ÷ (1 + r)^n
where r is the rate per period and n the number of periods.
In Excel, the workbook uses PV(Rate, Nper, Pmt, FV, Type) and FV(Rate, Nper, Pmt, Type), with the contribution entered as a negative number to signal an outflow, Type = 1 for payments at the start of a period and Type = 0 at the end. For a monthly contribution, divide the annual rate by 12 and multiply the years by 12.
A worked example
The workbook runs three cases. All three are worth being able to reproduce.
1. Inflating an expense forward. Mr X needs Rs 20,000 a month today. At 5 percent inflation, five years later the same basket costs
20,000 × (1.05)^5 = Rs 25,526 a month
2. Discounting it back. To have Rs 25,526 in five years, invested in a 5-year bank FD at a post-tax 8 percent, he does not need to set aside Rs 25,526 today:
PV = 25,526 ÷ (1.08)^5 = Rs 17,372
Rs 8,154 of the eventual sum is produced by the investment, not by the saver.
3. The cost of a five-year delay. X invests Rs 5,000 a month at 12 percent from age 30 to 60:
| Start age | Months | Corpus at 60 | Extra contributed |
|---|---|---|---|
| 30 | 360 | Rs 1,74,74,820 | — |
| 35 | 300 | Rs 93,94,233 | — |
| Difference | 60 | Rs 80,80,587 | Rs 3,00,000 |
Sixty extra instalments of Rs 5,000 — Rs 3 lakh of the saver's own money — are worth Rs 80.8 lakh at 60. That ratio, roughly 27 to 1, is the entire argument for starting early, and it is arithmetic rather than exhortation.
Why NISM asks about it
Chapter 1 (Fundamental Concepts in Retirement Planning), section 1.2.1, introduces this and Chapter 3 (Retirement Planning Process) applies it end to end in the deterministic corpus calculation of section 3.2.7. Expect direct computations — inflate an expense forward n years, discount a required sum back — and questions on which Excel inputs go where, including the sign convention and the Type flag. The conceptual question that recurs is why a delay in starting to save costs far more than the instalments missed.
Common exam traps
- Inflate first, then discount. The workbook's two-step corpus method inflates today's expense to the retirement date, and only then discounts the retirement income stream back to a lump sum. Doing it in one step with a net rate skips the first number the paper asks for.
- Match the rate to the period. A monthly contribution needs the annual rate divided by 12 and the years multiplied by 12. Feeding an annual rate into a monthly
Nperis the most common arithmetic error in this chapter. Typematters. Contributions at the beginning of the period (Type = 1) accumulate one extra period of return againstType = 0. On a 35-year series that is not a rounding difference.- The negative sign is not decoration. Excel returns the PV in the example as minus Rs 17,372 because it is an outflow. Read the magnitude, not the sign, but know why it is there.
- Time value is not the same as the real rate of return. Time value is the mechanism; the real rate is what you get after netting inflation off the nominal return. Use the second inside the first, not instead of it.
Where this is taught
- Series XIX-A · Chapter 6: Risk and Return - Investor and Fund Perspectiveintroduced here
- Series SEBI-ICE · Chapter 2: Key Concepts in personal financeintroduced here
- Series XVII · Chapter 1: Fundamental Concepts in Retirement Planningintroduced here
- Series XXI-A · Chapter 1: Investmentsintroduced here
- Series X-A · Chapter 2: Time Value of Moneyintroduced here
Related terms
- InflationA sustained general rise in the price level, which erodes what a rupee buys — and the reason a nominal return has to be deflated before it means anything.
- Real rate of returnThe return on an investment after the effect of inflation has been removed — what the money actually buys more of, as against the nominal percentage the product advertises.
- Present valueWhat a sum of money due in the future is worth today, found by discounting it back at the rate the money could earn: PV = FV ÷ (1 + r)^n.
- Compound interestInterest earned on the original amount and also on the interest already earned. Rs 1,000 at 9% grows to Rs 31,409 in 40 years compounded, against Rs 4,600 with simple interest.
- Future valueWhat a sum of money invested today will be worth at a future date once returns have been earned and reinvested — the compounding half of the time value of money.
- Economic Internal Rate of ReturnThe IRR of a project widened to include the direct and indirect economic benefits it creates, whether or not they reach the fund — as distinct from the financial IRR the fund actually earns.
- Present Value (PV) factorThe multiplier that converts a single future amount into today's value: 1 ÷ (1 + r)^n. At 14% for 8 years it is 0.351, so Rs 100 due then is worth Rs 35.10 now.
- Modified Internal Rate of ReturnA variant of IRR that discounts a fund's capital calls and compounds its distributions at the investor's opportunity cost, instead of assuming every cash flow earns the IRR itself.
- PV functionThe spreadsheet function that converts a stream of future payments into the single lump sum needed today — the tool the workbook uses to size a retirement corpus and a life insurance cover.
- PMT functionThe spreadsheet function that converts a target corpus into the fixed periodic saving needed to reach it — the arithmetic behind every "how much should I invest a month" answer.
- Simple interestInterest earned only on the amount you first put in (the principal). The interest is not added back, so it never earns interest of its own, unlike compound interest.
- Nominal returnThe stated rate of return quoted on an investment before adjusting for inflation — as opposed to the workbook's real rate of return, which accounts for it.
- Present Value Annuity FactorThe number that converts a level stream of equal payments for n periods into its present value at rate r: PVA(n, r) = (1 − (1 + r)^−n) / r. Used with the PV factor to value bonds.
- Opportunity CostThe benefit given up on the next-best alternative when money is committed to one investment instead of another — the yardstick an AIF return has to beat before it counts as a good return.
- Purchasing powerWhat a sum of money can actually buy in goods and services. Inflation reduces it, so the same rupee amount buys less the further in the future it is received.
- Retirement planningThe process of putting in place a roadmap for retirement: defining the income the envisaged lifestyle needs, sizing the corpus, and saving and investing to build and then draw it down.
- Years to retirementThe period from now to the retirement date, or retirement age minus current age. It drives both how much inflation raises future expenses and how long savings have to compound.
- Deterministic methodThe simplest way to calculate a retirement corpus — one fixed inflation rate and one fixed return throughout, giving a single definite corpus figure but ignoring how the sequence of returns can hurt a portfolio.
- Retirement corpusThe pool of money built up during a person's working years whose only job, after retirement, is to generate the income that used to come from a salary.
- SavingThe difference between money earned and money spent. Saving becomes investment only when that surplus is committed for a period in the expectation of getting back a larger amount.
- Required Rate of ReturnThe minimum return an investor expects before committing money: the nominal risk-free rate plus a risk premium. It is not a guaranteed, forecast or realised return.
- Real Risk-free RateThe basic return an investor demands purely for postponing consumption, assuming no inflation and no uncertainty about future cash flows — the pure time value of money.
- FV functionThe spreadsheet function that converts a stream of contributions, growing or fixed, into their value at a future date — the tool the workbook uses to project a retirement corpus and future living costs.
- PerpetuityA constant cash flow received every period with no end date. Its present value is simply the cash flow divided by the discount rate: PV = C / r.