Time value explained: this guide covers what it means, who it applies to, the step-by-step process, documents required, fees, due dates and penalties in India — so you can stay compliant with confidence and avoid costly mistakes.
A rupee today is worth more than a rupee a year from now, because today's rupee can earn interest or reduce a loan. Every offer that spreads payments over time, from a supplier's instalment plan to a bank loan, has to be judged with that fact in mind. The time value of money gives the tools: compounding, discounting, annuities and amortisation.
Future value = amount x (1 + r)^n. Present value = amount / (1 + r)^n. An annuity is an equal payment at the end of each period; its present value is the payment times the annuity factor [1 - (1 + r)^-n] / r. To compare offers, bring every payment to the same date, usually today, at a stated rate. The offer with the lower present value of payments costs less, whatever the total of rupees paid.
Simple and compound interest, and the effective rate
Most of the arithmetic below can be set up once in a financial model and reused for every offer that comes in.
Simple interest is paid only on the original sum: interest = principal x rate x time. Compound interest is paid on the principal and on interest already earned, so a sum grows to principal x (1 + r)^n. If interest is added more than once a year, the effective annual rate is higher than the stated one: effective rate = (1 + r/m)^m - 1, where m is the number of times a year interest is added. For an assumed nominal rate of 10 per cent: half-yearly gives (1.05)^2 - 1 = 10.25 per cent; quarterly gives (1.025)^4 - 1 = 10.38 per cent. When you compare two loans, compare effective rates.
Future value and present value
For one sum: future value FV = P x (1 + r)^n; present value PV = FV / (1 + r)^n. The factor 1 / (1 + r)^n is the discount factor. At an assumed 10 per cent, the factors for years 1 to 4 are 0.909, 0.826, 0.751 and 0.683, and ₹1 lakh grows to 1.4641, which is 1.464 lakh in four years.
For an uneven series, bring each amount to the present with its own factor and add them, as in capital budgeting with NPV. For an annuity of equal payments A for n years, PV = A x [1 - (1 + r)^-n] / r, and FV = A x [(1 + r)^n - 1] / r. At 10 per cent for four years the present value factor is 3.169 (the sum of the four factors above) and the future value factor is (1.4641 - 1) / 0.10 = 4.641.
A perpetuity is an equal payment for ever: PV = A / r. A payment of ₹50,000 a year at 10 per cent has a present value of 50,000 / 0.10 = ₹5,00,000.
Doubling period. A rule of thumb divides 72 by the rate in per cent: at 10 per cent money doubles in about 72 / 10 = 7.2 years (the exact figure is about 7.3 years).
| Formula | In words | Symbols |
|---|---|---|
| Future value | Principal grown at the rate for n periods | P x (1 + r)^n |
| Present value | Future sum divided by the growth factor | FV / (1 + r)^n |
| Annuity present value | Payment times annuity factor | A x [1 - (1 + r)^-n] / r |
| Annuity future value | Payment times accumulation factor | A x [(1 + r)^n - 1] / r |
| Perpetuity | Payment over the rate | A / r |
| Effective rate | Compounded rate for a year | (1 + r/m)^m - 1 |
Worked example 1: two payment offers
Rohan Printing Works, an invented firm, is offered a press by a supplier on two terms: Offer A, ₹8.40 lakh paid today; Offer B, ₹2.40 lakh at the end of each of four years (₹9.60 lakh in total). The owner's required return is assumed at 10 per cent. Discount factors are rounded to three decimals and present values to two.
| Year | Offer B payment (₹ lakh) | Factor at 10% | Present value |
|---|---|---|---|
| 1 | 2.40 | 0.909 | 2.18 |
| 2 | 2.40 | 0.826 | 1.98 |
| 3 | 2.40 | 0.751 | 1.80 |
| 4 | 2.40 | 0.683 | 1.64 |
| Total (unrounded values added) | 7.61 |
The four rows are rounded individually, so they add to 7.60; the total is taken from the unrounded values. Check with the annuity factor: 2.40 x 3.169 = 7.61. Offer B has a present value of ₹7.61 lakh against ₹8.40 lakh for Offer A, so B costs less in today's money by ₹0.79 lakh, even though the rupees paid add up to more (9.60 against 8.40). The owner takes Offer B, provided the supplier's price and the press are the same under both terms and the owner has no better use of cash that would change the required return. If the owner's required return were higher, B would look better still.
Worked example 2: loan amortisation
The owner also takes a loan of ₹10,00,000 to fund installation, repayable in four equal yearly instalments, at an assumed 12 per cent a year. The annuity factor is 3.03735, so the instalment = 10,00,000 / 3.03735 = ₹3,29,234 (rounded to the nearest rupee). Each instalment pays the interest on the balance first and the rest reduces the principal.
| Year | Opening balance | Interest at 12% | Instalment | Principal repaid | Closing balance |
|---|---|---|---|---|---|
| 1 | 10,00,000 | 1,20,000 | 3,29,234 | 2,09,234 | 7,90,766 |
| 2 | 7,90,766 | 94,892 | 3,29,234 | 2,34,342 | 5,56,424 |
| 3 | 5,56,424 | 66,771 | 3,29,234 | 2,62,463 | 2,93,961 |
| 4 | 2,93,961 | 35,275 | 3,29,236 | 2,93,961 | 0 |
The last instalment is ₹2 higher because of rounding; the balance closes to nil. Total paid = 3,29,234 x 3 + 3,29,236 = ₹13,16,938, of which interest is ₹3,16,938 (1,20,000 + 94,892 + 66,771 + 35,275 = 3,16,938). Interest falls each year as the balance falls, and the principal share rises. The schedule is also what a lender uses to show the outstanding amount at any date; for the tax treatment of interest, see our income-tax guides.
How to use the tools
- Compare payment plans by present value at the same rate.
- Compare loans by effective rate and total interest.
- Value a stream of regular receipts, such as rent, with the annuity factor.
- Use the rule of 72 to judge a rate quickly.
- Feed the factors into project appraisal and lease decisions; see lease or buy. The rate to use is discussed in cost of capital.
Common mistakes
- Comparing total rupees paid without discounting.
- Using a stated annual rate when interest is added monthly.
- Mixing end-of-year and start-of-year payments in the annuity factor.
- Using a rate that includes inflation for real cash flows, or the reverse.
- Forgetting that the balance in an amortisation schedule falls, so interest falls.
- Treating a rate used in an example as a current market rate.
Need help with payment and loan comparisons?
If you are weighing an instalment plan, a loan or a lease, our financial modeling service puts the options on one sheet at a common rate and shows present value, effective rate and the amortisation schedule. You can then change the rate or term and see the result at once.
Key takeaways
- A rupee today is worth more than a rupee later; compound forward and discount back.
- Present value of an annuity = payment x annuity factor.
- Compare offers by present value at a stated rate.
- Compare loans by effective rate; interest is highest in the first year of a reducing balance.
- The rule of 72 estimates the doubling time.
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Disclaimer: The methods described are standard cost accounting and financial management techniques. The worked example uses an invented business and invented figures, including any tax, interest or exchange rate, which are assumptions for illustration and not current rates. Where the article refers to a legal requirement, the linked guide and the official text should be checked. This article is general information, not legal advice; check the official text before acting.