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Quantitative Aptitude · Mathematics of Finance

Present Value, Future Value and Net Present Value for CA Foundation

Updated 1 October 2026 · Fact-checked

Future value is what money today grows to at an interest rate. Present value is what future money is worth today, found by dividing by (1 + i)^n. Net present value is the sum of the present values of all inflows minus the initial outlay. Accept a project if NPV is positive; reject it if negative.

Understand Present Value, Future Value and Net Present Value

Money today is worth more than the same amount later. You can invest it and earn interest. This is the time value of money, and everything in this topic follows from it.

Compounding moves money forward in time. If you invest ₹1,000 at 10% a year, you have ₹1,100 after one year. After two years you earn interest on ₹1,100, not on ₹1,000, so you have ₹1,210. The amount at the end is the future value (FV).

Discounting moves money backward in time. It is compounding in reverse. If ₹1,210 is due in two years and the rate is 10%, it is worth ₹1,000 today. That is the present value (PV). The rate used is called the discount rate.

To compare cash flows from different years, bring them all to the same date, usually today. Net present value (NPV) does this for a project. You discount every future inflow to today, add them up, and subtract the cash you spend at the start. A positive NPV means the project earns more than the discount rate. A negative NPV means it earns less.

In the exam, cash flows are usually taken at the end of each year unless the question says otherwise. The initial outlay is at time 0, so it is not discounted.

Key formulas to remember

Future value (annual compounding)
FV = P × (1 + i)^n
P = amount today, i = rate per year as a decimal, n = number of years.
Future value (m times a year)
FV = P × (1 + r ÷ m)^(m × n)
r = nominal annual rate, m = compounding periods per year. Use the rate per period (r ÷ m) and the number of periods (m × n).
Present value of a single amount
PV = FV ÷ (1 + i)^n
Same as FV × (1 + i)^(−n). Discounting is the reverse of compounding.
Net present value
NPV = C₁ ÷ (1 + i) + C₂ ÷ (1 + i)² + … + Cₙ ÷ (1 + i)ⁿ − C₀
C₁ to Cₙ are cash inflows at the end of years 1 to n. C₀ is the initial outlay at time 0.
NPV decision rule
NPV > 0: accept | NPV < 0: reject | NPV = 0: indifferent
Accepting means the project earns more than the discount rate. When choosing between projects, prefer the higher positive NPV.

How to solve Present Value, Future Value and Net Present Value questions

Use this order for any PV, FV or NPV question. It keeps timing and rates straight, which is where most marks are lost.

  1. 1Draw a timeline. Mark time 0, 1, 2 … n and write each cash flow under its year. Outflows are negative.
  2. 2Find the rate per period. If compounding is not annual, divide the annual rate by m and multiply the years by m.
  3. 3Decide the direction. Moving money forward to a later date means multiply by (1 + i)^n. Moving it back to an earlier date means divide by (1 + i)^n.
  4. 4For NPV, discount each inflow separately using its own year number. Do not discount the amount at time 0.
  5. 5Add the present values of the inflows, then subtract the initial outlay.
  6. 6State the sign of NPV and apply the rule: positive accept, negative reject.
  7. 7Match your answer with the options. If the question allows rounding, expect small differences in the last digits.

Quickest way: Option elimination and quick discounting

When to use it: Use it in MCQs. It saves time and avoids a wrong answer that costs 0.25 marks.

  1. Check direction first. A PV must be smaller than the future amount. An FV must be larger. This removes one or two options at once.
  2. For compounding more often than yearly, the answer must be slightly above the annual-compounding answer. Eliminate options equal to or below it.
  3. For NPV, estimate the sign first. Add the inflows without discounting. If even this total is below the outlay, NPV is negative. Skip the full calculation.
  4. Use clean numbers. Questions are usually built so that (1.1)² = 1.21 or (1.1)³ = 1.331. Divide by these directly.
  5. If the question gives a table of discount factors, multiply each cash flow by its factor and add. Do not recompute powers.
  6. If a question needs four or more years of discounting at an awkward rate and no table is given, mark it for the end.

Common mistakes in Present Value, Future Value and Net Present Value

  • Discounting the initial outlay

    Students apply the discount factor to every cash flow without checking its time.

    Fix: The outlay at time 0 has a discount factor of 1. Use it as it is.

  • Multiplying instead of dividing when finding PV

    The FV formula is memorised and used for every question.

    Fix: Ask whether the money is moving to a later date or an earlier date. Earlier means divide by (1 + i)^n.

  • Using the annual rate when compounding is quarterly or half-yearly

    The question mentions '12% p.a.' and students plug in 0.12 and n = 1.

    Fix: Use r ÷ m as the rate and m × n as the number of periods. For 12% quarterly for 1 year, use 3% for 4 periods.

  • Discounting every inflow by the same number of years

    Students find one discount factor and apply it to all inflows.

    Fix: The year 1 inflow uses (1 + i)¹, year 2 uses (1 + i)², and so on.

  • Reporting the wrong sign or a wrong decision

    Students subtract in the wrong order, writing outlay minus inflows.

    Fix: NPV = PV of inflows − outlay. A positive answer means accept. Check the sign against your quick estimate.

  • Confusing NPV with total profit

    Students add inflows and subtract the outlay without discounting.

    Fix: Undiscounted profit ignores the time value of money. NPV always uses discounted inflows.

Worked examples

Example 1

What is the present value of ₹1,21,000 receivable after 2 years, if money earns 10% p.a. compounded annually? Options: (A) ₹1,00,000 (B) ₹1,05,000 (C) ₹96,800 (D) ₹90,000

Show the solution
  1. Direction: the amount is in the future and you want today's value, so divide.
  2. PV = FV ÷ (1 + i)^n = 1,21,000 ÷ (1.10)².
  3. (1.10)² = 1.21.
  4. PV = 1,21,000 ÷ 1.21 = ₹1,00,000.
  5. Check: ₹1,00,000 grows to ₹1,10,000 after year 1 and ₹1,21,000 after year 2.

Answer: (A) ₹1,00,000

Example 2

A project needs an initial outlay of ₹1,00,000 and gives cash inflows of ₹60,000 at the end of year 1 and ₹60,000 at the end of year 2. The discount rate is 10%. What is the NPV, and what should you do? Options: (A) ₹4,132, accept (B) ₹20,000, accept (C) −₹4,132, reject (D) ₹14,132, accept

Show the solution
  1. Quick check: total inflows are ₹1,20,000, which is more than ₹1,00,000, so the NPV could be positive. Discounting is needed.
  2. PV of year 1 inflow = 60,000 ÷ 1.10 = ₹54,545.45.
  3. PV of year 2 inflow = 60,000 ÷ 1.21 = ₹49,586.78.
  4. Total PV of inflows = 54,545.45 + 49,586.78 = ₹1,04,132.23.
  5. NPV = 1,04,132.23 − 1,00,000 = ₹4,132.23, which is about ₹4,132.
  6. NPV is positive, so accept the project.
  7. Option B (₹20,000) is the undiscounted profit. Option C has the wrong sign.

Answer: (A) ₹4,132, accept

Example 3

What is the amount after 1 year if ₹50,000 is invested at 12% p.a. compounded quarterly? (Use (1.03)^4 = 1.1255) Options: (A) ₹56,000 (B) ₹56,275 (C) ₹55,000 (D) ₹57,000

Show the solution
  1. Rate per quarter = 12% ÷ 4 = 3%.
  2. Number of quarters = 4 × 1 = 4.
  3. FV = 50,000 × (1.03)^4 = 50,000 × 1.1255.
  4. FV = ₹56,275.
  5. Check: annual compounding at 12% gives ₹56,000. Quarterly compounding must give slightly more, so (A) is the trap and (B) fits.

Answer: (B) ₹56,275

Exam tips

  • Look at the compounding period first. Many questions say half-yearly or quarterly to test whether you adjust the rate and the number of periods.
  • In NPV questions, check whether the question gives discount factors. If it does, use them as given and do not recompute.
  • Do the sign test before heavy arithmetic. Direction and sign checks remove wrong options quickly, which protects you from negative marking.
  • Read whether the outlay is at the start of the project or at the end of year 1. Time 0 is not discounted.
  • If two projects are compared, calculate NPV for each and choose the higher positive one. Do not compare total inflows.

Practice questions from Mathematics of Finance

Present Value, Future Value and Net Present Value: frequently asked questions

What is the difference between present value and future value?

Future value is what an amount today will be worth later after earning interest. Present value is what an amount due later is worth today. They are linked by the same rate and time: FV = PV × (1 + i)^n.

How do I calculate NPV in CA Foundation?

Discount each year's cash inflow by dividing it by (1 + i)^t, where t is the year. Add these present values and subtract the initial outlay. The result is the NPV.

When do I accept or reject a project using NPV?

Accept it if NPV is positive, because the project earns more than the discount rate. Reject it if NPV is negative. If NPV is zero, the project earns exactly the discount rate and you are indifferent.

Is the initial investment discounted in NPV?

No, if it is made at time 0. Time 0 means today, so its present value is the amount itself. Only if the question places it in a later year do you discount it.

What discount rate should I use?

Use the rate given in the question. It stands for the return you could earn elsewhere or the cost of funds. Convert it to a rate per period if the compounding is not annual.