The Time Value of Money means:
Money today is worth more than the same amount of money in the future.
This happens because money today can:
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Be invested
-
Earn interest
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Grow over time
Example
If you have $1,000 today, you can invest it at 10% interest.
After 1 year it becomes:
1000 × 1.10 = $1,100
2. Why Time Value of Money Exists
So $1,000 today = $1,100 in one year.
There are several reasons:
Interest earning ability
Money can be invested to earn returns.
a) Inflation
Prices increase over time, so future money buys less.
b) Risk
Future payments are uncertain.
If you delay receiving money, you lose the opportunity to invest it.
3. Key Concepts of TVM
Present Value (PV)
The current value of money today.
Example
The value today of $1,000 received after 2 years.
Future Value (FV)
The value of money in the future after interest is added.
Example
How much $1,000 today will become after 3 years.
Interest Rate (r)
The percentage return earned per period.
Example
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5%
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8%
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10%
Time (n)
The number of years or periods.
Example
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3 years
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5 years
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10 years
4. Future Value Calculation
Formula:
FV = PV(1 + r)ⁿ
Example:
PV = 2,000
r = 10%
n = 3 years
FV = 2000(1.10)³
FV = 2,662
Meaning $2,000 today becomes $2,662 in 3 years.
5. Present Value Calculation
Formula:
PV = FV / (1 + r)ⁿ
Example:
FV = 2,662
r = 10%
n = 3
PV = 2662 / (1.10)³
PV = 2,000
This tells us the value today of future money.
6. Compounding
Compounding means interest is earned on both the original money and the previous interest.
Example
Year 1
1000 → 1100
Year 2
1100 → 1210
Year 3
1210 → 1331
Interest keeps building on itself.
7. Discounting
Discounting is the reverse of compounding.
Instead of moving forward to future value, we move backward to present value.
It helps to determine:
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Value of future payments
-
Value of investments
8. Applications of Time Value of Money
The concept is widely used in finance such as:
a) Loan calculations
Used to prepare loan repayment schedules.
b) Investment decisions
To determine whether an investment is profitable.
c) Capital budgeting
Businesses use it to evaluate projects.
d) Bond valuation
Used to determine the value of bonds.
e) Retirement planning
Helps calculate future savings.
9. Example Used in Exams
Example question:
You invest 5,000 at 8% for 4 years.
FV = 5000(1.08)⁴
FV = 6,802.44
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