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Banking and Insurance - Laws and Practice · Calculation of Interest and Annuities

Time Value of Money: Present and Future Value Explained

Updated 11 October 2026 · Fact-checked

Time value of money means a rupee today is worth more than a rupee later, because it can earn interest. Future value = P × (1 + r)^n moves money forward by compounding. Present value = FV ÷ (1 + r)^n moves money back by discounting. Use the same r and n units.

Understand Time Value of Money: Present and Future Value

A rupee in hand today can be deposited and earn interest. So ₹1,00,000 today is worth more than ₹1,00,000 a year from now. This is the time value of money. Banks, lenders and insurers use it to price loans, deposits and policies.

Compounding moves a sum forward in time. You add interest each period, and the next period's interest is earned on the new, larger balance. The result is the future value (FV).

Discounting moves a sum backward in time. You ask: what amount today would grow to the given future sum at the given rate? The result is the present value (PV). Discounting is compounding run in reverse.

The rate used in discounting is the discount rate. The factor 1 ÷ (1 + r)^n is the discount factor. It is always below 1 when r is positive and n is more than zero. Multiply a future sum by it to get the present value.

The rate and the period must match. If interest is compounded half-yearly, use the half-yearly rate and the number of half-years. This single point decides most marks in this topic.

Key rules to remember

Future value of a single sum (annual compounding)
FV = P × (1 + r)^n
P = amount today, r = rate per year as a decimal, n = number of years.
Present value of a single sum
PV = FV ÷ (1 + r)^n
Same r and n as the compounding formula, used in reverse.
Discount factor
DF = 1 ÷ (1 + r)^n
PV = FV × DF. Questions often give DF values in a table.
Compounding more than once a year
FV = P × (1 + r ÷ m)^(m × n)
m = compounding periods per year. r is the nominal annual rate.
Effective annual rate
EAR = (1 + r ÷ m)^m − 1
Use it to compare rates with different compounding frequencies.
Present value of several future sums
PV = Σ [CFt ÷ (1 + r)^t]
Discount each cash flow separately, then add.

How to solve Time Value of Money: Present and Future Value questions

Use this method for any question on future value, present value or discount factors.

  1. 1Identify what is asked: the value today (PV) or the value at a future date (FV).
  2. 2List the given data: amount, annual rate, time in years, and how often interest is compounded.
  3. 3Convert the rate and time to the same period. For half-yearly compounding, use r ÷ 2 and 2n.
  4. 4Choose the formula: multiply by (1 + i)^N to go forward, divide by it (or multiply by the discount factor) to go back.
  5. 5If discount factors are supplied, use them instead of computing powers.
  6. 6Calculate step by step and show the working. Keep at least four decimals in factors until the final step.
  7. 7For several cash flows, discount each one separately and add the results.
  8. 8State the answer in rupees with a one-line conclusion, such as which option is better.

Quickest way: Direction and period check

When to use it: When time is short and the question gives a rate, a period and one sum.

  1. Ask: am I moving forward or backward? Forward means multiply, backward means divide.
  2. Write the per-period rate i and the number of periods N first.
  3. Compute (1 + i)^N once, using repeated multiplication for small N.
  4. Apply: FV = P × factor, or PV = FV ÷ factor.
  5. Sense-check: FV must exceed P, and PV must be below FV.

Common mistakes in Time Value of Money: Present and Future Value

  • Dividing when you should multiply, or the reverse.

    Students memorise formulas without picturing the direction of time.

    Fix: Future value is always larger than today's sum, present value always smaller (for a positive rate). Check this before you write the answer.

  • Using the annual rate with half-yearly or quarterly compounding.

    The question states the rate per annum and students plug it in directly.

    Fix: Divide the rate by m and multiply the years by m before using the formula.

  • Entering the rate as 10 instead of 0.10.

    Mixing percentage and decimal forms.

    Fix: Write (1 + 0.10) every time, never (1 + 10).

  • Treating compound growth as simple interest, FV = P(1 + rn).

    Simple interest is learnt first and feels familiar.

    Fix: If interest is earned on interest, the power form is needed. Use simple interest only when the question says so.

  • Discounting a series of cash flows with a single factor.

    Students apply the first year's factor to all amounts.

    Fix: Each cash flow gets the factor for its own year.

  • Rounding discount factors too early.

    Trying to save time.

    Fix: Keep four decimals and round only the final rupee figure.

Worked examples

Example 1

A customer deposits ₹2,00,000 in a bank at 8% per annum compounded annually. What will it grow to after 3 years?

Show the solution
  1. P = ₹2,00,000, r = 0.08, n = 3, annual compounding.
  2. FV = 2,00,000 × (1.08)^3.
  3. (1.08)^2 = 1.1664. (1.08)^3 = 1.1664 × 1.08 = 1.259712.
  4. FV = 2,00,000 × 1.259712 = ₹2,51,942.40.

Answer: The deposit grows to ₹2,51,942.40 after 3 years (interest earned is ₹51,942.40).

Example 2

A company will receive ₹5,00,000 after 2 years. The discount rate is 10% per annum. Find the present value. Also state whether it is better to take ₹4,00,000 today or wait for this sum.

Show the solution
  1. FV = ₹5,00,000, r = 0.10, n = 2.
  2. Discount factor = 1 ÷ (1.10)^2 = 1 ÷ 1.21 = 0.826446.
  3. PV = 5,00,000 × 0.826446 = ₹4,13,223 (approx.). Check: 5,00,000 ÷ 1.21 = 4,13,223.14.
  4. Compare: the present value of the future receipt is ₹4,13,223, which is above ₹4,00,000.

Answer: The present value is about ₹4,13,223. At a 10% discount rate, waiting for ₹5,00,000 is better than taking ₹4,00,000 today.

Exam tips

  • Show the formula, the substituted values and the final figure. Marks are given for method even if arithmetic slips.
  • Read the compounding frequency in the first line. Underline it before you start.
  • When discount factors are given in the question, use them as given. Do not recompute powers.
  • In decision questions, finish with a clear recommendation based on present values at the same date.
  • Write the rate as a decimal inside the bracket to avoid slips.

Practice questions from Calculation of Interest and Annuities

Time Value of Money: Present and Future Value in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Time Value of Money: Present and Future Value: frequently asked questions

What is the difference between compounding and discounting?

Compounding moves a present sum forward to find its future value by adding interest on interest. Discounting moves a future sum back to today to find its present value. They use the same rate and period, but in opposite directions.

How do I calculate present value with a discount rate?

Divide the future sum by (1 + r)^n, or multiply it by the discount factor 1 ÷ (1 + r)^n. For example, ₹1,10,000 due in one year at 10% has a present value of ₹1,00,000.

What changes if interest is compounded half-yearly?

Use half the annual rate and twice the number of years. At 8% for 3 years, use 4% for 6 periods. The result is slightly higher than with annual compounding.

Is future value the same as compound interest?

Future value is the total amount at the end, principal plus interest. Compound interest is only the interest part, which is FV − P.