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Financial Management and Business Data Analytics · Time Value of Money

Future Value and Present Value of a Single Cash Flow

Updated 10 October 2026 · Fact-checked

Future value is what a lump sum grows to after n periods at rate r: FV = PV × (1 + r)^n. Present value is today's worth of a future sum: PV = FV ÷ (1 + r)^n. Match the rate to the period, get the factor from the formula or table, then multiply.

Understand Future Value and Present Value of a Single Cash Flow

Money today is worth more than the same money later, because today's money can be invested and earn a return. This is the time value of money. Every other topic in this chapter builds on the single-sum case.

Future value (FV) answers: if I invest ₹1,00,000 today at 10% a year, what will it be worth in 5 years? Each year the interest is added to the balance, and next year's interest is earned on the larger balance. This is compounding. One year multiplies the amount by (1 + r). After n years, you multiply n times, which gives (1 + r)^n.

Present value (PV) runs the process backwards. If you will receive ₹5,00,000 after 4 years, what is it worth today? You divide by (1 + r) for each year. This is discounting, and the rate used is the discount rate (your opportunity cost, or the rate given in the question).

The factor (1 + r)^n is the FV factor. Its reciprocal, 1 ÷ (1 + r)^n, is the PV factor. Exam tables list these factors for different rates (columns) and periods (rows), so you can look them up instead of computing powers. The table value is usually rounded to three or four decimals, so your answer may differ slightly from an exact calculation. Use the table if the question gives one.

The rate and the period must be in the same unit. If interest is compounded half-yearly, use the half-yearly rate and the number of half-years.

Key rules to remember

Future value of a single sum
FV = PV × (1 + r)^n
r is the rate per period and n is the number of periods. (1 + r)^n is the FV factor.
Present value of a single sum
PV = FV ÷ (1 + r)^n = FV × PV factor
PV factor = 1 ÷ (1 + r)^n. Always smaller than 1 for r > 0.
Relation between the factors
PV factor = 1 ÷ FV factor
Use it to get one factor when only the other is given in the table.
More than one compounding a year
FV = PV × (1 + r ÷ m)^(m × n)
r is the annual nominal rate, m is the number of compounding periods per year, n is years.
Effective annual rate
EAR = (1 + r ÷ m)^m − 1
Use it to compare rates compounded at different frequencies.

How to solve Future Value and Present Value of a Single Cash Flow questions

Use this sequence for any single-sum question, whether it asks for FV, PV, or a decision between two amounts.

  1. 1Decide the direction. Moving a sum forward in time means FV (multiply). Moving it back to today means PV (discount).
  2. 2Note the amount, the annual rate and the time in years, and check the compounding frequency (annual, half-yearly, quarterly).
  3. 3Convert the rate and time to the same period. For half-yearly compounding, use r ÷ 2 and n × 2.
  4. 4Pick the factor. Use the table value for the rate and period if given. Otherwise compute (1 + r)^n.
  5. 5Multiply: FV = PV × FV factor, or PV = FV × PV factor. Show the factor and the substitution.
  6. 6Do a sense check. FV must be larger than PV, and PV must be smaller than the future amount.
  7. 7If the question asks for a decision, compare the amounts at the same point in time (usually today) and state the conclusion in words.

Quickest way: Factor-first method

When to use it: Use it when the question gives a factor table or a simple rate and few periods. It saves time in numericals worth many marks.

  1. Write the period rate and number of periods first, for example 10%, 5 periods.
  2. Read the factor from the table at that column and row. Write it down with its name (FV factor or PV factor).
  3. Multiply the amount by the factor in one line.
  4. If only the FV factor is given and you need PV, divide by it. If only the PV factor is given and you need FV, divide by it.
  5. Check the direction: FV is larger, PV is smaller. If not, you used the wrong factor.

Common mistakes in Future Value and Present Value of a Single Cash Flow

  • Using the annual rate and years when interest is compounded half-yearly or quarterly.

    Students copy the rate and time from the question without reading the compounding frequency.

    Fix: Divide the rate by the number of compounding periods per year and multiply the years by the same number before looking up the factor.

  • Multiplying by the PV factor when FV is asked, or the reverse.

    The two table columns look alike and students are in a hurry.

    Fix: Decide the direction first. FV needs a factor above 1, and PV needs a factor below 1. Do the sense check at the end.

  • Calculating simple interest, PV × (1 + r × n), instead of compound growth.

    Simple interest is familiar from school, and the question may not say compound clearly.

    Fix: In this topic, treat interest as compounded unless the question says simple interest. Use (1 + r)^n.

  • Reading the wrong row or column in the factor table.

    Tables have many numbers close together, and students mix up period and rate.

    Fix: Put a finger on the rate column and the period row separately, then read the intersection. Write the factor next to its label.

  • Rounding the factor too early or too much.

    Students trim the factor to two decimals to make multiplication easier.

    Fix: Keep at least four decimals when computing yourself. If a table value is given, use it as printed.

  • Comparing amounts that fall at different dates.

    In decision questions, students compare ₹1,50,000 today with ₹2,40,000 later without discounting.

    Fix: Bring both amounts to the same date, usually the present, and then compare. State the decision clearly.

Worked examples

Example 1

Mr Verma invests ₹2,00,000 for 3 years at 8% per annum. Find the amount at the end of 3 years if interest is compounded (a) annually and (b) half-yearly.

Show the solution
  1. Direction: moving forward in time, so use FV = PV × (1 + r)^n.
  2. (a) Annual compounding: r = 8%, n = 3. FV factor = (1.08)^3 = 1.259712.
  3. FV = 2,00,000 × 1.259712 = ₹2,51,942.40.
  4. (b) Half-yearly compounding: rate per period = 8% ÷ 2 = 4%, periods = 3 × 2 = 6.
  5. FV factor = (1.04)^6 = 1.265319 (approximately).
  6. FV = 2,00,000 × 1.265319 = ₹2,53,063.80.
  7. Sense check: both are above ₹2,00,000, and more frequent compounding gives a slightly higher amount.

Answer: (a) ₹2,51,942 (approximately, ₹2,51,942.40). (b) ₹2,53,064 (approximately, ₹2,53,063.80). Half-yearly compounding gives about ₹1,121 more.

Example 2

Ms Iyer is offered ₹1,50,000 today or ₹2,40,000 after 4 years. Her opportunity cost of funds is 12% per annum compounded annually. The PV factor at 12% for 4 years from the table is 0.636. Which option should she choose?

Show the solution
  1. Compare both options at the same date, today. ₹1,50,000 is already a present value.
  2. Discount ₹2,40,000 for 4 years at 12% using the table: PV = FV × PV factor.
  3. PV = 2,40,000 × 0.636 = ₹1,52,640.
  4. Compare: ₹1,52,640 is higher than ₹1,50,000, so the later amount is worth more in today's terms.
  5. Check with the formula: 1 ÷ (1.12)^4 = 1 ÷ 1.573519 = 0.6355, so PV is about ₹1,52,525. The conclusion is the same.
  6. Sense check: the PV of the future sum is less than ₹2,40,000, as it should be.

Answer: She should choose ₹2,40,000 after 4 years. Its present value is ₹1,52,640 using the table factor, which is ₹2,640 more than ₹1,50,000.

Exam tips

  • Write the formula and the factor before multiplying. Step marks go to the method even if the table value is misread.
  • Use the table values given in the question paper and do not recompute them. Small differences from exact answers are expected.
  • Read the compounding frequency in the question before touching the table. This is the most common trap.
  • In decision questions, end with a clear sentence stating the choice and why, for example the PV is higher than the amount offered today.
  • For MCQs, use the sense check. If the question asks for FV, remove any option smaller than the principal.

Practice questions from Time Value of Money

Future Value and Present Value of a Single Cash Flow in other exams

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

Future Value and Present Value of a Single Cash Flow: frequently asked questions

What is the formula for the future value of a single sum?

FV = PV × (1 + r)^n, where r is the interest rate per period and n is the number of periods. For example, ₹1,00,000 at 10% for 5 years gives ₹1,00,000 × 1.61051 = ₹1,61,051.

How do I use the present value factor table in CMA Intermediate?

Find the column for the discount rate and the row for the number of periods. The number at the intersection is the PV factor. Multiply the future amount by it to get the present value.

What changes when interest is compounded half-yearly or quarterly?

Divide the annual rate by the number of periods in a year and multiply the years by the same number. For 8% for 3 years compounded half-yearly, use 4% for 6 periods.

Why is the present value always less than the future value?

Because money can earn a return over time, a rupee received later is worth less than a rupee today. Discounting at a positive rate reduces the future amount, so the PV factor is below 1.