Time Value of Money: Compounding, Discounting, Annuities, EMI and Rule of 72 for RBI Grade B Finance

Last updated: 2026-11-13 · MockMentor

The time value of money is not a separate line in the RBI Grade B Finance syllabus, but it sits underneath several lines that are: bond pricing in financial markets, project appraisal in alternate sources of finance and PPP, and numericals in accounting and financial statements. Objective questions test compounding, effective interest rates, annuities and the Rule of 72, often as quick calculations. This chapter explains the concept and every formula you need, with worked examples.

In one line: a rupee today is worth more than a rupee in the future because it can be invested to earn interest; compounding finds the future value of money today, and discounting finds the present value of money to be received later.

Basic concepts

• Time value of money (TVM): the idea that money available now is worth more than the same amount in the future, because of its earning capacity.
• Present value (PV): the value today of a sum to be received in the future, found by discounting.
• Future value (FV): the value at a future date of a sum invested today, found by compounding.
• Interest rate (r): the return for lending money, or the cost of borrowing it, per period.
• Discount rate: the rate used to bring future cash flows to present value; it reflects the opportunity cost of money and risk.
• Annuity: a series of equal payments made at regular intervals for a fixed number of periods.

Why in News?

1. RBI's repo rate hike to 5.50% in October 2026 raised the rates at which future cash flows are discounted, which lowers the present value of bonds and long-term projects.
2. Rising inflation, with CPI inflation at 5.54% in September 2026, reduces the real value of future money, a core idea of TVM.
3. Accounting and finance numericals, which use TVM in areas such as bond pricing and project appraisal, were the largest Finance topic in the 2026 RBI Grade B Phase 2 objective paper.
4. Home loan EMIs, which are annuity calculations, change for borrowers on floating rate loans linked to the repo rate.

Why money has time value

1. Investment opportunity: money today can be invested to earn a return.
2. Inflation: prices rise over time, so the same money buys less in future.
3. Risk and uncertainty: a future payment may not be received.
4. Preference for present consumption: people generally prefer to consume now rather than later.

Simple and compound interest

Simple interest

Interest is calculated only on the original principal.

Simple Interest (SI) = P × R × T ÷ 100

Amount = P + SI

Example: ₹20,000 at 6% simple interest for 3 years. SI = 20,000 × 6 × 3 ÷ 100 = ₹3,600. Amount = ₹23,600.

Compound interest

Interest is calculated on the principal plus interest already earned (interest on interest).

Amount (A) = P × (1 + r)^n

Compound Interest = A − P

Example: ₹20,000 at 6% compounded annually for 3 years. A = 20,000 × (1.06)^3 = 20,000 × 1.191016 = ₹23,820.32. Compound interest = ₹3,820.32, which is ₹220.32 more than simple interest.

Compounding more than once a year

If interest is compounded m times a year at an annual rate r for n years:

A = P × (1 + r/m)^(m × n)

Example: ₹10,000 at 12% a year for one year.

More frequent compounding gives a higher amount.

Effective annual rate

The effective annual rate (EAR or effective interest rate) is the actual annual rate after taking compounding into account.

EAR = (1 + r/m)^m − 1

Example: 12% compounded quarterly. EAR = (1.03)^4 − 1 = 12.55%. The 12% is the nominal or stated rate.

With continuous compounding, EAR = e^r − 1, where e ≈ 2.71828. At 12%, this is about 12.75%.

Compounding and discounting

The term (1 + r)^n is the future value factor or compound value factor, and 1 ÷ (1 + r)^n is the present value factor or discount factor. Tables of these factors are used to save calculation time.

Example of discounting: how much should be invested today at 8% to get ₹50,000 after 5 years? PV = 50,000 ÷ (1.08)^5 = 50,000 ÷ 1.4693 = ₹34,029.

Practical uses

• Comparing options with cash flows at different times, such as taking a lump sum now or instalments later.
• Pricing bonds, by discounting coupons and principal.
• Project appraisal through net present value.
• Fixing loan EMIs and insurance premiums.
• Retirement and education planning.

Annuities

Types

Future value of an ordinary annuity

FV = A × [(1 + r)^n − 1] ÷ r

Example: ₹10,000 is invested at the end of every year for 5 years at 8%. FV = 10,000 × [(1.08)^5 − 1] ÷ 0.08 = 10,000 × 5.8666 = ₹58,666.

Future value of an annuity due

FV (annuity due) = FV (ordinary annuity) × (1 + r)

Using the same figures, but paid at the start of each year: 58,666 × 1.08 = ₹63,359.

Present value of an ordinary annuity

PV = A × [1 − (1 + r)^−n] ÷ r

Example: what is the present value of ₹10,000 received at the end of every year for 5 years at 8%? PV = 10,000 × [1 − 1 ÷ 1.4693] ÷ 0.08 = 10,000 × 3.9927 = ₹39,927.

Present value of an annuity due

PV (annuity due) = PV (ordinary annuity) × (1 + r) = 39,927 × 1.08 = ₹43,121.

Perpetuity

PV of a perpetuity = A ÷ r

Example: a perpetual payment of ₹5,000 a year at 10% has a present value of 5,000 ÷ 0.10 = ₹50,000.

PV of a growing perpetuity = A ÷ (r − g), where g is the growth rate and r > g.

Example: a dividend of ₹10 next year, expected to grow at 5% a year, with a required return of 12%: value = 10 ÷ (0.12 − 0.05) = ₹142.86. This is the Gordon growth model for valuing shares.

Loan EMI

An equated monthly instalment (EMI) is an ordinary annuity whose present value equals the loan amount.

EMI = P × r × (1 + r)^n ÷ [(1 + r)^n − 1]

where r is the monthly interest rate and n the number of months.

Example: a loan of ₹10 lakh for 10 years at 9% a year. Monthly rate = 0.75% = 0.0075; n = 120.

(1.0075)^120 ≈ 2.4514

EMI = 10,00,000 × 0.0075 × 2.4514 ÷ (2.4514 − 1) = 18,385.5 ÷ 1.4514 ≈ ₹12,668.

Total paid = 12,668 × 120 ≈ ₹15.2 lakh, of which about ₹5.2 lakh is interest. In the early years, most of each EMI goes towards interest; later, more goes towards principal.

Net present value and internal rate of return

TVM is the basis of capital budgeting.

• Net Present Value (NPV): the present value of future cash inflows minus the initial investment. A project is acceptable if NPV is positive.
• Internal Rate of Return (IRR): the discount rate at which NPV is zero. A project is acceptable if IRR is higher than the cost of capital.

Example: a project costs ₹1,00,000 and gives ₹40,000 at the end of each year for 3 years. At a discount rate of 10%, PV of inflows = 40,000 × 2.4869 = ₹99,474. NPV = 99,474 − 1,00,000 = −₹526. The project is not acceptable at 10%; its IRR is a little below 10% (about 9.7%).

Rules of thumb: 72, 114 and 144

The rule of 72 can also be used for inflation: at 6% inflation, prices double in about 12 years, so money loses half its value. It can also find the rate needed: to double money in 6 years, a rate of about 72 ÷ 6 = 12% is needed. The rules are approximations based on compound interest and work best for rates between about 6% and 10%.

More annuity situations

Deferred annuity

A deferred annuity starts after a gap. Its present value is found in two steps: value the annuity at the point just before payments start, then discount that value back to today.

Example: ₹20,000 a year for 4 years, with the first payment at the end of year 4 (so payments come in years 4, 5, 6 and 7), at 10%.

• PV of the 4-year annuity at the end of year 3 = 20,000 × [1 − (1.10)^−4] ÷ 0.10 = 20,000 × 3.1699 = ₹63,397.
• Discount 3 years to today: 63,397 ÷ (1.10)^3 = 63,397 ÷ 1.331 = ₹47,631.

Sinking fund

A sinking fund is money set aside regularly to repay a debt or replace an asset at a future date. The yearly amount is found from the future value of an annuity.

Annual instalment = Target amount × r ÷ [(1 + r)^n − 1]

Example: a company must repay a bond of ₹1 crore in 5 years and can invest at 8%. Instalment = 1,00,00,000 × 0.08 ÷ [(1.08)^5 − 1] = 8,00,000 ÷ 0.4693 = about ₹17.05 lakh a year.

Capital recovery factor

The capital recovery factor turns a present sum into an equal yearly amount over n years: r × (1 + r)^n ÷ [(1 + r)^n − 1]. It is the same formula as the EMI, applied annually, and banks use it to fix instalments on term loans.

Loan amortisation schedule

An amortisation schedule shows how each instalment is split between interest and principal.

Example: a loan of ₹1,00,000 at 10% a year, repaid in 3 equal annual instalments.

Instalment = 1,00,000 × 0.10 × (1.10)^3 ÷ [(1.10)^3 − 1] = 13,310 ÷ 0.331 = ₹40,211.

The interest part falls each year and the principal part rises, because interest is charged only on the balance still outstanding. This is why prepaying a loan early saves the most interest.

Effect of a rate change on a floating rate loan

When the repo rate rises and an EBLR-linked loan resets, a bank can either raise the EMI or keep the EMI and extend the tenure. RBI asked lenders in 2023 to give borrowers the choice and to explain clearly how a rate change affects the EMI and tenure, after many borrowers found their loan tenures stretched without notice.

Nominal rate, APR and effective rate in practice

Lenders often quote a flat rate or a monthly rate, which hides the true cost.

• Flat rate: interest is charged on the original loan amount for the whole period, even though the balance falls. A flat rate of 10% on a 3-year loan costs much more than a 10% reducing-balance rate, roughly 18% in effective terms.
• Annual Percentage Rate (APR): the all-in annual cost of a loan, including processing fees and charges. RBI's rules on Key Fact Statements require lenders to show the APR for retail and MSME loans.
• Monthly rate: 1.5% a month sounds small but equals an effective annual rate of (1.015)^12 − 1 = 19.6%.

Example: a credit card charges 3.5% a month on unpaid balances. Effective annual rate = (1.035)^12 − 1 = 51.1%.

Present value and the value of assets

TVM underlies the valuation of almost every financial asset.

Because the discount rate sits in the denominator, a rise in interest rates lowers the present value of all these assets. That is why stock and bond markets often fall when RBI raises rates, and why long-dated assets fall the most.

Practice problems with answers

1. ₹50,000 is invested for 2 years at 8% compounded half-yearly. Find the amount. Answer: 50,000 × (1.04)^4 = ₹58,493.
2. What is the effective annual rate of 9% compounded monthly? Answer: (1.0075)^12 − 1 = 9.38%.
3. How much must be invested today at 7% to receive ₹1 lakh in 10 years? Answer: 1,00,000 ÷ (1.07)^10 = 1,00,000 ÷ 1.9672 = ₹50,835.
4. A scheme pays ₹12,000 at the end of every year for ever. If the discount rate is 8%, what is it worth today? Answer: 12,000 ÷ 0.08 = ₹1,50,000.
5. An investor saves ₹5,000 at the start of every year for 3 years at 10%. What is the amount at the end of year 3? Answer: annuity due = 5,000 × [(1.10)^3 − 1] ÷ 0.10 × 1.10 = 5,000 × 3.31 × 1.10 = ₹18,205.
6. Using the Rule of 72, at what rate will money double in 8 years? Answer: 72 ÷ 8 = 9%.
7. A deposit pays 6.5% when inflation is 5%. What is the approximate real return? Answer: about 1.5%; exactly, 1.065 ÷ 1.05 − 1 = 1.43%.

Real and nominal rates

The nominal interest rate includes inflation; the real rate removes it.

Exact formula: (1 + nominal) = (1 + real) × (1 + inflation)

Approximate (Fisher equation): Real rate ≈ Nominal rate − Inflation rate

Example: a fixed deposit pays 7% when inflation is 5.5%. The real return is about 1.5%. More exactly, 1.07 ÷ 1.055 − 1 = 1.42%.

Common mistakes

• Using the annual rate and number of years when payments are monthly; both must match the period.
• Confusing ordinary annuities with annuities due.
• Forgetting that a higher discount rate lowers present value.
• Treating the Rule of 72 as exact.

Possible exam and interview questions

1. Explain the concept of the time value of money and its use in bond pricing and project appraisal. (620 words)
2. Distinguish between an ordinary annuity and an annuity due, with formulas and an example. (420 words)
3. Find the effective annual rate of 10% compounded half-yearly.
4. Using the Rule of 72, how long will it take for money to double at 9%? How long to triple using the Rule of 114?
5. Interview: Why do higher interest rates reduce the value of long-term bonds and shares?

Related reading: bond market, alternate sources of finance, and inflation.

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