Time value of money
₹1 today is worth more than ₹1 later. TVM is the maths that converts between the two.
Time value of money (TVM) is the idea that ₹1 today is worth more than ₹1 received later, because today's rupee can be invested and earn a return. Every financial plan rests on it: how much a goal will cost, how much to save each month, and what a future sum is worth now.
It is Chapter 2 of the NISM Series X-A curriculum, straight after the introduction to financial planning, and the later chapters on goals, loans and retirement all reuse it.
The five numbers in every TVM problem
Any TVM question gives you four of these and asks for the fifth.
- PV (present value)
- What a sum is worth today.
- FV (future value)
- What a sum grows to after a number of periods at a given rate.
- r (rate per period)
- The return or interest rate for one period. A 12% annual rate paid monthly is 1% per month.
- n (number of periods)
- How many compounding periods. Ten years of monthly payments is 120 periods.
- PMT (payment)
- A fixed amount paid or received every period, such as a SIP instalment or a loan EMI.
The formulas
Future value of a lump sum
Formula
FV = PV × (1 + r)^n
Used for
What a deposit grows to
Present value of a lump sum
Formula
PV = FV ÷ (1 + r)^n
Used for
What a future goal costs in today's money
Future value of a regular payment (ordinary annuity)
Formula
FV = PMT × [((1 + r)^n − 1) ÷ r]
Used for
Corpus from a monthly SIP
Present value of a regular payment (ordinary annuity)
Formula
PV = PMT × [(1 − (1 + r)^−n) ÷ r]
Used for
Loan amount an EMI supports; corpus needed for a pension
Effective annual rate
Formula
EAR = (1 + i/m)^m − 1
Used for
Comparing rates compounded at different frequencies
| To find | Formula | Used for |
|---|---|---|
| Future value of a lump sum | FV = PV × (1 + r)^n | What a deposit grows to |
| Present value of a lump sum | PV = FV ÷ (1 + r)^n | What a future goal costs in today's money |
| Future value of a regular payment (ordinary annuity) | FV = PMT × [((1 + r)^n − 1) ÷ r] | Corpus from a monthly SIP |
| Present value of a regular payment (ordinary annuity) | PV = PMT × [(1 − (1 + r)^−n) ÷ r] | Loan amount an EMI supports; corpus needed for a pension |
| Effective annual rate | EAR = (1 + i/m)^m − 1 | Comparing rates compounded at different frequencies |
Worked examples
Illustrative rates, chosen for round numbers. They are not return forecasts.
- 1
1. Future value
₹1,00,000 invested at 8% a year for 10 years: 1,00,000 × 1.08^10 = about ₹2,15,892.
- 2
2. Present value of a goal
A course costing ₹10,00,000 in 6 years, discounted at 10%: 10,00,000 ÷ 1.10^6 = about ₹5,64,474 needed today.
- 3
3. Monthly saving
₹10,000 a month for 10 years at 12% a year (1% a month, 120 months): 10,000 × [(1.01^120 − 1) ÷ 0.01] = about ₹23,00,387.
- 4
4. Effective rate
A deposit at 9% compounded quarterly earns (1 + 0.09/4)^4 − 1 = about 9.31% a year, more than a 9% annual-compounding deposit.
Free account, this exam preselected.
Annuity due versus ordinary annuity
An ordinary annuity pays at the end of each period; an annuity due pays at the start. Rent and insurance premiums are usually paid in advance, so they are annuities due. Multiply the ordinary-annuity answer by (1 + r) to convert. Questions often hinge on this one word: 'beginning' or 'end'.
How X-A tests this
TVM shows up two ways: as a single calculation MCQ, and as one step inside a caselet where a client's goal must be costed and then funded. X-A carries 150 marks with a pass at 90 out of 150 (60%) and negative marking, so a wrong number costs more than a skipped one.
The traps: using an annual rate with monthly periods, forgetting to inflate a goal before discounting it, and mixing up annuity due and ordinary annuity. Answer options are usually built from exactly these mistakes, so a quick sanity check on the size of the answer catches most of them.
FAQs
What is time value of money in simple words?expand_more
Money today is worth more than the same amount later, because it can be invested and grow. TVM is the maths that converts amounts between today and the future.
What is the formula for future value?expand_more
For a lump sum, FV = PV × (1 + r)^n, where r is the rate per period and n the number of periods. Regular payments use the annuity formula instead.
What is the difference between present value and future value?expand_more
Present value brings a future amount back to today by discounting. Future value takes today's amount forward by compounding. They are the same formula solved in opposite directions.
Why does compounding frequency matter?expand_more
More frequent compounding adds interest on interest sooner, so the effective annual rate rises above the stated rate. 9% compounded quarterly is about 9.31% a year.
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