Time Value of Money for NISM certification
A rupee today is worth more than a rupee next year, because today's rupee can be invested. Every planning calculation in X-A (goal corpus, SIP needed, EMI, retirement income, bond price) rests on this one idea. This chapter builds the toolkit: present and future value, CAGR, EMIs, loan periods, annuities and perpetuities, with the spreadsheet functions you will have in the exam hall.
Advice & ResearchSeries X-A63 MCQs5 lessons20 flashcards3 memory tricks
Practise Time Value of Money free
What you'll learn
- Why money has time value
Explain why ₹100 today is worth more than ₹100 later, and name the inputs to any TVM problem. - Present value and future value
Calculate PV and FV of a single sum, and see how compounding frequency changes the result. - Rate of return: CAGR
Convert a start value and an end value into a compound annual growth rate. - EMIs and loan periods
Use PMT for instalments and NPER for the number of instalments. - Annuities and perpetuities
Value a stream of equal payments, paid at the end or the start of each period, or forever.
Key formulas
| Future value | FV = PV × (1 + r)^n |
|---|---|
| Present value | PV = FV ÷ (1 + r)^n |
| r and n | Rate per period and number of periods: for quarterly compounding at 8% a year, r = 2% and n = years × 4 |
| CAGR | (End value ÷ Beginning value)^(1/n) − 1 |
| Period under a year or odd days | Use n = days ÷ 365, i.e. raise to the power 365/days |
| Spreadsheet | =RATE(nper, pmt, pv, fv), e.g. =RATE(6, 0, -100000, 200000) |
| EMI | =PMT(rate/12, months, −loan) |
| Number of instalments | =NPER(rate/12, −EMI, loan) |
Concepts explained
Time value of money
Money today is worth more than the same money later because it can earn a return; amounts at different dates must be moved to one date before comparing.
What it means
- Compounding moves money forward: FV = PV × (1 + r)^n.
- Discounting moves money back: PV = FV ÷ (1 + r)^n.
- Higher rates and longer waits lower PV.
- Goal ₹50,000 in 4 years
- Rate 8%
- 50,000 ÷ 1.3605
Answer: ₹36,751 needed today
Related terms
- CAGR: c-xa-cagr
CAGR
The constant yearly compound rate that turns a beginning value into an end value.
What it means
- (End ÷ Beginning)^(1/n) − 1.
- For holding periods in days, raise to 365/days.
- Simple averaging of total return overstates it.
- 2^(1/6) = 1.1225
Answer: 12.25% a year, not 16.7%
Annuity, annuity due and perpetuity
Equal payments at regular intervals; paid at period-end (ordinary) or period-start (due); a perpetuity never ends.
What it means
- PV ordinary = C × [1 − (1 + r)^−n] ÷ r.
- Annuity due = ordinary × (1 + r).
- Perpetuity = C ÷ r.
- Ordinary: ₹39,927
- Due: × 1.08
Answer: ₹43,121
Exam tip: Spreadsheet type 0 = end of period, type 1 = beginning.
Memory tricks
FV = PV × (1 + r)^n; PV = FV ÷ (1 + r)^n.
Annuity due flows come at the beginning and are worth more to the receiver.
Years to double ≈ 72 ÷ rate %.
Try 3 NISM-style questions
Q1. Why would a person making payments prefer an ordinary annuity to an annuity due?
- They keep the money for an extra period and can earn on it
- Ordinary annuities have lower total payments
- Annuity due payments are not allowed for individuals
- Ordinary annuities avoid all interest costs
Show answer
Answer: (1) They keep the money for an extra period and can earn on it
Paying at the end lets the payer use the money during the period.
Q2. A flat costs ₹60 lakh now, or ₹20 lakh now plus ₹9 lakh at each year-end for 5 years. At 8%, the instalment plan's present value is about
- ₹65.0 lakh
- ₹60.0 lakh
- ₹55.9 lakh
- ₹35.9 lakh
Show answer
Answer: (3) ₹55.9 lakh
20 + 9 × 3.9927 = ₹55.9 lakh, so the instalment plan is cheaper in today's money.
Q3. An annuity is
- A single lump sum received at maturity
- A payment that grows every year without a limit
- Any irregular stream of cash flows
- A series of equal payments at regular intervals
Show answer
Answer: (4) A series of equal payments at regular intervals
Pensions and fixed interest payments are common examples.
Practise all 63 questions Free · explanations for every option · see where you go wrong