What is Time Value of Money? Future value, Present value, Annuity explained for BBA/MBA Students

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Ever heard the saying, “a rupee today is worth more than a rupee tomorrow”? That’s the single most important idea in all of finance. It’s called the Time Value of Money (TVM), and mastering it is essential for your BBA or MBA exams and your future career.

But what does it really mean?

Simply put, money you have right now is more valuable than the exact same amount in the future. Why? Because you can invest it. That ₹100 you have today could be put in a bank to earn interest, turning it into ₹105 by next year.

This article will break down all the core TVM concepts, formulas, and examples you need to know.

1. Simple vs. Compound Interest: The Two Ways Money Grows

First, let’s understand interest. It’s the fee you pay for borrowing money or the reward you get for saving it. The starting amount is called the Principal (P). (the amount which you give to the bank and gets interest onto it)

What is Simple Interest?

Simple interest is the most basic form. It’s calculated only on the original principal amount.

  • Simple Interest Formula: Interest = P * i * n

    • P = Principal

    • i = Interest rate

    • n = Number of time periods

  • Example: You lend ₹10,000 at 3% simple interest per quarter.

    • Interest per quarter: ₹10,000 * 0.03 * 1 = ₹300

    • Total interest over 5 years (20 quarters): ₹300 * 20 = ₹6,000

What is Compound Interest?

This is where the magic happens. Compound interest is calculated on the principal plus all the interest you’ve already earned. You start earning “interest on your interest.”

  • Example: You invest ₹1,000 at 6% interest compounded annually.

    • End of Year 1: ₹1,000 * 1.06 = ₹1,060

    • End of Year 2: ₹1,060 * 1.06 = ₹1,123.60

      • Notice you earned ₹63.60 in year 2, not just ₹60. That extra ₹3.60 is 6% interest on the ₹60 you earned in year 1.

Key Takeaway: The more frequently interest is compounded (e.g., monthly vs. annually), the faster your money grows.

2. Future Value (FV): What Will Your Money Be Worth?

Future Value (FV) tells you what a single amount of money today will be worth at a specific point in the future. This process is called compounding.

This answers the question: “If I invest ₹X today, how much will I have in 5 years?”

Future Value Formula (for a Single Amount)

FV = P * (1 + i)^n

  • FV = Future Value

  • P = Principal (or Present Value)

  • i = Interest rate per period

  • n = Number of periods

FV Example

  • Problem: A company invests ₹40,00,000 for 5 years at 16% per year, compounded semi-annually. What is the future value?

  • Solution:

    • P: ₹40,00,000

    • i: 16% / 2 = 8% per period (0.08)

    • n: 5 years * 2 periods per year = 10 periods

    • Calculation: FV = 40,00,000 * (1 + 0.08)^10

    • FV = ₹86,35,680

3. Present Value (PV): What is Future Money Worth Today?

Present Value (PV) is the exact opposite of FV. It tells you what a future amount of money is worth in today’s terms. This process is called discounting.

This answers the question: “I need to have ₹5,00,000 in 10 years. How much do I need to invest today to get there?”

Present Value Formula (for a Single Amount)

PV = FV / (1 + i)^n

  • PV = Present Value

  • FV = Future Value (the amount you want in the future)

  • i = Discount rate (interest rate) per period

  • n = Number of periods

PV Example

  • Problem: You need ₹2,00,000 in 4 years. How much must you invest today if the interest rate is 16% compounded semi-annually?

  • Solution:

    • FV: ₹2,00,000

    • i: 16% / 2 = 8% per period (0.08)

    • n: 4 years * 2 periods per year = 8 periods

    • Calculation: PV = 2,00,000 / (1 + 0.08)^8

    • PV = ₹108,054

      • This means ₹108,054 invested today at 8% per period will grow to ₹2,00,000 in 4 years.

4. Annuities: The Power of Equal Payments

An Annuity is simply a series of equal payments made at equal time intervals. Think of a car loan, a mortgage payment, or a regular monthly saving plan.

  • Ordinary Annuity: Payments are made at the end of each period (this is the most common type).

Future Value of an Annuity (FVA)

This tells you the total value of a stream of regular payments at a future date.

  • Formula: FVA = R * [((1 + i)^n - 1) / i]

  • R = Rent (the amount of each equal payment)

  • Example: You invest ₹50,000 every year for 5 years in a fund that earns 11% annually. How much will you have at the end?

    • R: ₹50,000

    • i: 0.11

    • n: 5

    • Calculation: FVA = 50,000 * [((1 + 0.11)^5 - 1) / 0.11]

    • FVA = ₹311,390

Present Value of an Annuity (PVA)

This tells you the value today of a series of future payments. This is how loan amounts are calculated and how lottery jackpots are valued.

  • Formula: PVA = R * [(1 - (1 + i)^-n) / i]

  • R = Rent (the amount of each payment)

  • Example: A retirement plan offers you ₹5,00,000 per year for 32 years. The interest rate is 9%. How much would you need to pay for this plan today?

    • R: ₹5,00,000

    • i: 0.09

    • n: 32

    • Calculation: PVA = 5,00,000 * [(1 - (1 + 0.09)^-32) / 0.09]

    • PVA = ₹52,04,000 (approx.)

5. Perpetuities: An Annuity That Lasts Forever

A Perpetuity is a special type of annuity where the equal payments continue forever.

Present Value of a Perpetuity Formula

There is no future value (it’s infinite!), but the present value is surprisingly simple.

PV = C / i

  • C = Cash flow (payment) per period

  • i = Interest rate (or discount rate)

  • Example: What is the present value of an investment that pays ₹500 every year, forever, if the discount rate is 5%?

    • C: ₹500

    • i: 0.05

    • Calculation: PV = 500 / 0.05 = ₹10,000

      • This means ₹10,000 invested today at 5% would pay you ₹500 every year without ever touching the principal.

6. Quick Tools: Growth Rate & The Doubling Rules

How to Calculate Compound Growth Rate

This formula finds the average annual growth rate (r) of something (like sales or dividends) over time.

  • Formula: Vn = Vo * (1 + r)^n

    • Vn = Ending Value

    • Vo = Starting Value

    • n = Number of periods

    • (You must solve for r)

  • Example: A dividend grows from ₹21 to ₹31 over 5 years. The growth rate (r) is 8.09%.

Quick Doubling Period Rules

Need a fast way to estimate how long it takes for an investment to double? Use these rules.

  1. Rule of 72: A simple and popular estimate.

    • Formula: Years to Double ≈ 72 / i (use the whole number interest rate)

    • Example: At 10% interest, your money will double in 72 / 10 = 7.2 years.

  2. Rule of 69: A slightly more accurate formula.

    • Formula: Years to Double ≈ 0.35 + (69 / i)

    • Example: At 10% interest: 0.35 + (69 / 10) = 7.25 years.