Time Value of Money Formula Explained with Examples

Why a few formulas cover almost everything

Time value of money problems look different on the surface. One is about an FD, another about a SIP, another about a home loan. Underneath, they share the same few formulas. Learn these and you can answer most money-over-time questions on your own.

Below, each formula is explained in plain words, with an Indian example. You can test every answer on a time value of money calculator.

This is educational content and not financial advice. Rates in examples are assumptions, not current offers. Check RBI, your bank and official sources for live rates.

Formula 1: future value of a lump sum

FV = PV x (1 + r / m)^(m x t)

• PV: the amount invested today
• r: the yearly interest rate as a decimal
• m: how many times a year interest is added (1 for yearly, 4 for quarterly, 12 for monthly)
• t: the number of years

If interest is added once a year, the formula becomes FV = PV x (1 + r)^t. The more often interest is added, the more you earn, though the difference is small at normal rates.

Worked example 1: an FD with quarterly compounding

Rakesh puts Rs. 5,00,000 in a 3-year FD at 7% a year, compounded quarterly. This is an assumed rate.

• Quarterly rate = 7% / 4 = 1.75% = 0.0175
• Number of quarters = 3 x 4 = 12
• 1.0175^12 = 1.231439 (rounded)
• FV = 5,00,000 x 1.231439 = Rs. 6,15,720 (rounded)

With yearly compounding, he would get 5,00,000 x 1.07^3 = 5,00,000 x 1.225043 = about Rs. 6,12,522. So quarterly compounding adds around Rs. 3,198. Many Indian bank FDs compound quarterly, so check your own FD terms.

Formula 2: present value and the discount rate

PV = FV / (1 + r)^n

This is just Formula 1 turned upside down. It answers the question: what is a future sum worth today? A higher discount rate gives a lower present value, because a high return makes today’s money more powerful.

For example, Rs. 1,00,000 to be received 3 years from now, with a 6% discount rate, has a present value of 1,00,000 / 1.06^3 = 1,00,000 / 1.191016 = Rs. 83,962 (rounded). That is why a promise of money later is worth less than the same amount today.

Formula 3: future value of regular payments

FV = PMT x [((1 + i)^n – 1) / i]

• PMT: the payment made each period
• i: the rate per period (yearly rate divided by 12 for monthly)
• n: the total number of periods

This is the ordinary annuity formula, where payments are made at the end of each period. For payments at the start of each period (an annuity due), multiply the result by (1 + i).

Worked example 2: how big a SIP for Rs. 1 crore?

Nisha wants Rs. 1,00,00,000 in 15 years. She assumes 12% a year. What monthly SIP does she need? Rearrange the formula: PMT = FV x i / ((1 + i)^n – 1).

• i = 12% / 12 = 0.01
• n = 15 x 12 = 180
• 1.01^180 = 5.99581 (rounded)
• (5.99581 – 1) / 0.01 = 499.581
• PMT = 1,00,00,000 / 499.581 = Rs. 20,017 (rounded)

She would need about Rs. 20,017 a month. Her total investment would be about Rs. 36.03 lakh (Rs. 20,017 x 180), and the rest of the Rs. 1 crore comes from assumed growth. Because returns are not guaranteed, she should test lower rates too. At 10%, the monthly amount would be higher.

Key takeaway: Rearranging the same formula lets you solve for the SIP amount, the time or the rate. Only one item should be unknown at a time.

Formula 4: the EMI formula

EMI = P x i x (1 + i)^n / ((1 + i)^n – 1)

A loan is a present value problem. The bank gives you the loan amount P today, and you repay it in equal monthly instalments. The EMI is the payment that makes the present value of all those instalments equal to the loan.

Worked example 3: a home loan EMI

Suresh takes a Rs. 20,00,000 loan for 20 years at 9% a year. The rate is only an illustration. Lenders link their rates to the RBI repo rate or other benchmarks, and these change over time.

• Monthly rate i = 9% / 12 = 0.75% = 0.0075
• n = 20 x 12 = 240
• (1.0075)^240 = 6.00916 (rounded)
• EMI = 20,00,000 x 0.0075 x 6.00916 / (6.00916 – 1)
• EMI = 15,000 x 6.00916 / 5.00916 = 15,000 x 1.199637 = Rs. 17,995 (rounded)

His total repayment is about 17,995 x 240 = Rs. 43,18,800, so he pays roughly Rs. 23.19 lakh as interest. Because of the time value of money, the early EMIs are mostly interest and the later ones mostly principal. This is why a small prepayment in the early years saves a large amount of interest.

Formula 5: effective annual rate

EAR = (1 + r / m)^m – 1

The nominal rate is the number printed on the offer. The effective annual rate (EAR) is what you really earn in one year after compounding. Take a nominal 8% compounded quarterly: (1 + 0.08 / 4)^4 – 1 = 1.02^4 – 1 = 1.082432 – 1 = 8.24%.

A nominal 12% compounded monthly gives 1.01^12 – 1 = 1.126825 – 1 = 12.68%. When you compare two products, compare their EAR, not their nominal rates. It is the only fair way if they compound at different frequencies.

Formula 6: Rule of 72 and real return

The Rule of 72 is a mental shortcut. Divide 72 by the yearly return in percent to get the approximate years needed to double your money. At 8% it is 72 / 8 = 9 years. The exact check is 1.08^9 = 1.999, which is very close to 2.

The real return removes inflation: Real return = (1 + nominal) / (1 + inflation) – 1. With an 8% nominal return and 6% inflation, real return = 1.08 / 1.06 – 1 = 1.89%. MoSPI publishes CPI inflation data each month, so you can check the latest figure before you choose an assumption.

Dates matter too. If your investment starts mid-month, count the exact term with a date and time calculator before you decide n.

All the formulas in one table

Formula	Use	Example result
FV = PV x (1 + r/m)^(m x t)	Lump sum growth	Rs. 5 lakh at 7% quarterly for 3 years = Rs. 6,15,720
PV = FV / (1 + r)^n	Discounting	Rs. 1 lakh in 3 years at 6% = Rs. 83,962
FV = PMT x [((1+i)^n – 1)/i]	SIP or RD growth	Rs. 20,017 a month for 15 years at 12% = Rs. 1 crore
EMI formula	Loan instalment	Rs. 20 lakh at 9% for 20 years = Rs. 17,995
EAR = (1 + r/m)^m – 1	True yearly rate	8% quarterly = 8.24%
72 / rate	Doubling time	8% = about 9 years

Benefits of knowing the formulas

• You can check a bank or app calculation instead of trusting it blindly.
• You can compare products with different compounding on equal terms.
• You can solve for the one number you do not know: rate, time, payment or goal.
• You can see how a small change in rate or time changes the final value.
• You can plan loan prepayments with a clearer idea of interest saved.

Challenges and limitations

Formulas assume a fixed rate and regular payments. Real life is not that tidy. Floating-rate loans change when the lender revises its rate. Equity returns vary every year. A SIP may be missed in a tough month. Taxes, charges and exit loads are not in the basic formulas.

The formulas also assume you know the rate in advance, but nobody does. The best use of them is to explore scenarios, not to predict the future. Use ranges, and stay within what is realistic for the risk you take.

Common mistakes

• Using the yearly rate with monthly periods. Divide the rate by 12 when you use 12 periods a year.
• Forgetting the annuity due adjustment. Payments at the start of a period earn one extra period of growth.
• Comparing nominal rates. Compare EAR for a fair view.
• Treating the Rule of 72 as exact. It is a rough guide, best between 6% and 12%.
• Dropping decimals early. A tiny rounding of (1 + r)^n can change a crore-level answer by thousands.
• Ignoring tax and costs. Net return is lower than the headline return.

Best practices

• Write the formula and label each input before using numbers.
• Keep the rate period and the payment period the same.
• Test at least three rates: cautious, base and optimistic.
• Check your hand result with a trusted calculator.
• Use official sources, such as RBI for repo rate and MoSPI for inflation, to set assumptions.
• Read scheme documents from AMFI-registered fund houses for risk details.

Conclusion

Six formulas explain most of personal finance: future value, present value, annuity, EMI, effective rate and the Rule of 72. They all rest on one idea: money changes in value as time passes. Practise the three examples above, then try your own numbers. You will find that you understand FDs, SIPs and loans far better, and you will ask sharper questions of anyone selling you a product.

This is for information only and is not financial advice. Returns are not guaranteed.

Frequently Asked Questions

What is the basic time value of money formula?

The basic formula is FV = PV x (1 + r)^n. It tells you what a sum today will be worth after n periods at rate r. Present value is found by dividing instead of multiplying.

How is the EMI formula related to TVM?

An EMI is the equal payment whose present value equals the loan amount. So the EMI formula is an annuity present value formula solved for the payment.

What is the difference between nominal and effective rate?

The nominal rate is the stated yearly rate. The effective rate includes the effect of compounding within the year. An 8% nominal rate compounded quarterly is an effective rate of 8.24%.

Is the Rule of 72 accurate?

It is a good estimate for rates between about 6% and 12%. At 8%, it gives 9 years, and the exact figure is very close to that. For exact work, use the full formula.

Do these formulas work for PPF and NPS?

They work as approximations if you use the right rate and period. PPF rates are set by the government, and NPS returns depend on market performance, so always run more than one scenario.