NISM-Series-X-A: Investment Adviser (Level 1) · Time Value of Money

Future Value and Present Value of a Lump Sum

Updated 11 October 2026 · Fact-checked

Future value (FV) is what a lump sum today grows to after compounding at a rate for some periods: FV = PV × (1 + r)ⁿ. Present value (PV) is today's worth of a future amount: PV = FV ÷ (1 + r)ⁿ. Match the rate and the period unit, then apply the formula.

Understand Future Value and Present Value

Money today is worth more than the same amount later. You can invest it and earn a return. This is the time value of money, and every future value (FV) and present value (PV) question rests on it.

Future value answers: if I invest ₹X today at a rate r, what will it be worth after n periods? Each period's interest is added to the balance, and the next period earns interest on the larger balance. This is compounding. That is why the amount is multiplied by (1 + r) once for every period.

Present value runs the same logic backwards. If you will receive a sum in the future, you divide by (1 + r) once for each period to find what it is worth today. This is discounting. The rate used is called the discount rate.

FV and PV are two views of one relationship. A higher rate or a longer time raises FV and lowers PV. If you can do one, you can do the other by rearranging the formula.

The exam tests whether you match the rate to the period. If interest is compounded half-yearly, quarterly or monthly, you divide the annual rate by the number of periods in a year and multiply the years by the same number.

Key formulas to remember

Future value of a lump sum: FV = PV × (1 + r)ⁿ; r is the rate per period as a decimal. n is the number of periods.
Present value of a lump sum: PV = FV ÷ (1 + r)ⁿ; Also written PV = FV × (1 + r)⁻ⁿ. The rate r is the discount rate per period.
Non-annual compounding: FV = PV × (1 + r ÷ m)^(m × t); r is the annual rate, m is compounding periods per year, t is years.
Solving for rate: r = (FV ÷ PV)^(1 ÷ n) − 1; Gives the rate per period. Use it for implied return questions.
Solving for number of periods: n = ln(FV ÷ PV) ÷ ln(1 + r); Rarely needed in full. Usually you test the options in the formula.

How to solve Future Value and Present Value questions

Use this method for any lump sum question on FV or PV.

1Identify what is asked: FV (growing forward) or PV (discounting back).
2List the given values: amount, annual rate, years and compounding frequency.
3Convert the rate and time to the same period. For half-yearly, use r ÷ 2 and 2 × t periods.
4Write the right formula: multiply by (1 + r)ⁿ for FV, divide by (1 + r)ⁿ for PV.
5Compute (1 + r)ⁿ carefully, step by step, or use the factor if given.
6Apply it to the amount and round only at the end.
7Sense check: FV must exceed PV and PV must be below FV when the rate is positive.

Quickest way: Estimate, then match the option

When to use it: Use when four options are spread apart and you have little time.

Decide direction first. Compounding means the answer is bigger. Discounting means it is smaller. This removes two options at once.
Compute (1 + r)ⁿ by repeated multiplication for small n, such as 1.10 → 1.21 → 1.331.
Use the Rule of 72 to check: money doubles in about 72 ÷ rate(%) years.
Pick the option nearest to your estimate, then confirm only if two options are close.

Common mistakes in Future Value and Present Value

Using the annual rate and number of years when compounding is half-yearly or quarterly.
Students read the rate as given and forget the frequency.
Fix: Divide the rate by m and multiply the years by m before using the formula.
Multiplying PV by (1 + r) × n instead of raising to power n.
This confuses compound growth with simple interest.
Fix: Compound means repeated multiplication. Use (1 + r)ⁿ. Simple interest uses 1 + r × n.
Multiplying instead of dividing when finding present value.
Students memorise one formula and apply it to every question.
Fix: Ask whether the cash is in the future. If yes, divide by (1 + r)ⁿ.
Using the rate as a whole number, such as 8 instead of 0.08.
Rushing and skipping the conversion.
Fix: Always write r as a decimal inside the bracket: 1 + 0.08.
Counting the wrong number of periods, such as including the starting year.
Timelines are read as calendar years instead of intervals.
Fix: Count intervals between the dates. Money invested today and withdrawn after 3 years has n = 3.
Rounding (1 + r)ⁿ too early.
It makes the calculation quicker.
Fix: Keep at least four decimals in the factor and round the final answer.

Worked examples

Example 1

You invest ₹1,00,000 today at 10% per annum compounded annually. What is its value after 3 years?

Show the solution

This asks for FV, so use FV = PV × (1 + r)ⁿ.
PV = ₹1,00,000, r = 0.10, n = 3.
(1.10)³ = 1.10 × 1.10 × 1.10 = 1.331.
FV = 1,00,000 × 1.331 = ₹1,33,100.

Answer: ₹1,33,100

Example 2

A client will receive ₹2,42,000 after 2 years. The discount rate is 10% per annum compounded annually. What is the present value?

Show the solution

This asks for PV, so use PV = FV ÷ (1 + r)ⁿ.
FV = ₹2,42,000, r = 0.10, n = 2.
(1.10)² = 1.21.
PV = 2,42,000 ÷ 1.21 = ₹2,00,000.
Check: 2,00,000 × 1.21 = 2,42,000, which matches.

Answer: ₹2,00,000

Exam tips

Read the compounding frequency before anything else. Half-yearly or quarterly wording is a favourite trap.
Check direction first. If the question asks for today's value of a future sum, the answer must be smaller than the future sum.
In caselets, the same data can feed several questions. Compute (1 + r)ⁿ once and reuse it.
Wrong answers cost a percentage of the marks for that question. On 2-mark questions, avoid guessing when you cannot narrow the options.
Expect the trap options to be the simple interest answer and the answer that multiplies instead of divides.

Practice questions from Time Value of Money

Future Value and Present Value 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: frequently asked questions

What is the difference between future value and present value?

Future value is the worth of money at a later date after it earns returns. Present value is the worth today of money to be received later. They use the same rate and period, with FV multiplying and PV dividing by (1 + r)ⁿ.

How do I calculate future value of a lump sum?

Multiply the amount by (1 + r)ⁿ, with r as the rate per period in decimal and n as the number of periods. For ₹50,000 at 8% for 2 years, FV = 50,000 × 1.08 × 1.08 = ₹58,320.

What happens if compounding is more frequent than yearly?

Divide the annual rate by the number of periods per year and multiply the years by the same number. More frequent compounding gives a slightly higher future value for the same annual rate.

Does a higher discount rate increase or decrease present value?

It decreases it. A higher rate means future cash is divided by a bigger factor, so it is worth less today.