Time Value of Money — 10 Solved Examples for JAIIB AFM (2026)
Step-by-step solutions to the most common TVM problems in JAIIB AFM: compound interest, present value, EMI calculation, Rule of 72, annuity, and NPV with exam-style questions.
Time Value of Money (TVM) is the foundation of JAIIB AFM Module C. Every exam has 5-8 questions on TVM concepts — compound interest, present value, EMI, and NPV. Here are 10 solved examples in the exact format you will see in the exam.
Core Concept: Why ₹100 Today ≠ ₹100 Tomorrow
Money has time value because it can earn interest. ₹100 today is worth more than ₹100 received after 1 year because you could invest today's ₹100 and have more than ₹100 after a year. This simple concept drives all TVM calculations.
Example 1: Simple Interest
Question: A bank offers a Fixed Deposit at 7% p.a. simple interest. If you deposit ₹50,000 for 3 years, what is the maturity amount?
Solution:
SI = P × R × T / 100
SI = 50,000 × 7 × 3 / 100 = ₹10,500
Maturity Amount = 50,000 + 10,500 = ₹60,500
Example 2: Compound Interest
Question: ₹1,00,000 is invested at 10% p.a. compounded annually for 3 years. Find the compound interest.
Solution:
FV = PV × (1 + r)ⁿ
FV = 1,00,000 × (1.10)³
FV = 1,00,000 × 1.331 = ₹1,33,100
Compound Interest = 1,33,100 - 1,00,000 = ₹33,100
Note: If this were simple interest, it would be ₹30,000. The extra ₹3,100 is the "interest on interest" effect.
Example 3: Present Value (Discounting)
Question: You need ₹5,00,000 after 5 years. If the discount rate is 8% p.a., how much should you invest today?
Solution:
PV = FV / (1 + r)ⁿ
PV = 5,00,000 / (1.08)⁵
PV = 5,00,000 / 1.4693
PV = ₹3,40,290 (approximately)
Interpretation: Invest ₹3.40 lakh today at 8% and it will grow to ₹5 lakh in 5 years.
Example 4: Rule of 72 (Quick Doubling Time)
Question: At what rate of interest will money double in 6 years (approximately)?
Solution:
Rule of 72: Doubling Time = 72 / Rate%
6 = 72 / Rate
Rate = 72 / 6 = 12% p.a.
Exam tip: If the question says "approximately" or "quick estimate", use Rule of 72. Exact answer would need logarithms.
Example 5: EMI Calculation
Question: A home loan of ₹30,00,000 at 9% p.a. for 20 years. Calculate the monthly EMI.
Solution:
EMI = P × r × (1+r)ⁿ / [(1+r)ⁿ - 1]
P = 30,00,000; r = 9%/12 = 0.75% = 0.0075; n = 20×12 = 240 months
(1.0075)²⁴⁰ = 6.009 (approx)
EMI = 30,00,000 × 0.0075 × 6.009 / (6.009 - 1)
EMI = 30,00,000 × 0.04507 / 5.009
EMI = 1,35,210 / 5.009 = ₹26,992 (approximately ₹27,000)
In the exam, options will be rounded. If you get ₹26,992, look for the closest option (₹26,992 or ₹27,000).
Example 6: Net Present Value (NPV)
Question: A project requires an investment of ₹10,00,000 and generates cash flows of ₹4,00,000 per year for 4 years. Cost of capital is 10%. Should the project be accepted?
Solution:
NPV = Sum of [CF/(1+r)^t] - Initial Investment
Year 1: 4,00,000 / 1.10 = 3,63,636
Year 2: 4,00,000 / 1.21 = 3,30,579
Year 3: 4,00,000 / 1.331 = 3,00,526
Year 4: 4,00,000 / 1.4641 = 2,73,205
Total PV of inflows = 12,67,946
NPV = 12,67,946 - 10,00,000 = +₹2,67,946
Decision: ACCEPT (NPV is positive)
Rule: NPV > 0 → Accept; NPV < 0 → Reject; NPV = 0 → Indifferent
Example 7: Payback Period
Question: Using the same project as Example 6 (₹10 lakh investment, ₹4 lakh annual cash flow), what is the payback period?
Solution:
Payback Period = Initial Investment / Annual Cash Flow
= 10,00,000 / 4,00,000
= 2.5 years
Note: This is the simple payback period (ignores time value). Discounted payback period would be longer.
Example 8: Future Value of Annuity (SIP Calculation)
Question: If you invest ₹10,000 per month in a mutual fund SIP earning 12% p.a. for 10 years, what will be the corpus?
Solution:
FV of Annuity = PMT × [(1+r)ⁿ - 1] / r
PMT = 10,000; r = 12%/12 = 1% = 0.01; n = 10×12 = 120 months
(1.01)¹²⁰ = 3.30 (approx)
FV = 10,000 × [3.30 - 1] / 0.01
FV = 10,000 × 230 = ₹23,00,000 (approximately ₹23.23 lakh)
Total invested: ₹12 lakh (₹10K × 120 months). Returns: ₹11+ lakh. This is the power of compounding.
Example 9: Effective Rate of Interest
Question: A bank offers 8% p.a. compounded quarterly. What is the effective annual rate?
Solution:
Effective Rate = (1 + r/n)ⁿ - 1
= (1 + 0.08/4)⁴ - 1
= (1.02)⁴ - 1
= 1.0824 - 1 = 0.0824
= 8.24% per annum
The effective rate is always higher than nominal rate when compounding is more frequent than annually.
Example 10: Profitability Index
Question: A project costs ₹5,00,000. PV of future cash flows is ₹6,50,000. Calculate Profitability Index and decide.
Solution:
PI = PV of future cash flows / Initial Investment
PI = 6,50,000 / 5,00,000 = 1.30
Decision: ACCEPT (PI > 1)
Rule: PI > 1 → Accept; PI < 1 → Reject; PI = 1 → Indifferent. PI of 1.30 means every ₹1 invested generates ₹1.30 in present value terms.
Quick Reference: Decision Rules
| Method | Accept If | Reject If |
|---|---|---|
| NPV | NPV > 0 | NPV < 0 |
| IRR | IRR > Cost of Capital | IRR < Cost of Capital |
| PI | PI > 1 | PI < 1 |
| Payback | Payback < Cutoff period | Payback > Cutoff period |
Exam Tips for TVM Questions
- Memorize (1.1)² = 1.21 and (1.1)³ = 1.331 — these appear in almost every NPV question with 10% discount rate
- Use Rule of 72 for approximations — saves 30 seconds on doubling/tripling time questions
- Convert annual rate to monthly for EMI — divide by 12 (not by 365)
- NPV is the most reliable method — if NPV and IRR conflict, NPV decision prevails (per theory)
- In the exam, use the on-screen calculator — don't waste time on mental math for powers
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FAQs
How do I choose between PV and FV formulas in JAIIB questions?
Use present value when the question asks what a future sum is worth today. Use future value when the question asks what a present sum will grow into after a given period.
Why do annuity questions confuse students so often?
Confusion usually comes from mixing ordinary annuity with annuity due and from unclear timing of payments. Always note whether the first payment happens immediately or at the end of the period before selecting the formula.
What calculator habits help in TVM questions?
Practice entering the sequence of keys in the same order every time so you avoid missing steps under pressure. Write down the given values first and then solve slowly to reduce errors in interest conversion and period matching.
Which TVM variation is tested most often in JAIIB?
Questions built around loans, deposits, and equated installments appear very often because they link math with banking use. Master EMI logic, present value of installments, and comparison of options to handle most variations with confidence.
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