2. Content
Time Value of Money
Classification of TVM
TVM Formula
Annuity
Types of Annuity
Cash Flow Diagram
Benefits of TVM
Identifying TVM Problems
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3. Time Value of Money (TVM)
Definition:
In the evolution of time ,the difference in the fundamental difference is
amount of time value of money. Everybody know that, at present any
amount of money is more than valuable from future amount. Time value of
money establish by this time preference.
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4. Classification of TVM
The four basic time value of money concepts are:
Future value of a sum
Present value of a sum
Future value of an annuity
Present value of an annuity
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5. TVM Formula
FV=Future value of money
PV=Present value of money
i = Interest rate
n = Number of compounding periods per year
t = Number of year
TVM: 𝑭𝑽 = 𝑷𝑽(𝟏 +
𝒊
𝒏
)(𝒏×𝒕)
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6. Future Value
Future value is the value of resource at a specific date. This is used in time
value of money calculations.
Future value = FV
𝑭𝑽 𝑵 = 𝑷𝑽(𝟏 + 𝑰) 𝑵
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7. Present Value
Value in the present of a total of money, in line to some future value it will
have when it has been invested at compound interest. This is a used in time
value of money calculations.
Present value = PV
𝑷𝑽 =
𝑭𝑽 𝑵
(𝟏+𝑰) 𝑵
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8. Annuity
An annuity is a series of equal payments or receipts that occur at evenly
spaced intervals for a specified period. The annuity values are assumed to
occur at the end of each period.
Examples of annuities:
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9. Types of Annuity
The two basic types of annuities are:
Ordinary annuity: With an ordinary annuity, the first payment takes place one
period in the future.
Annuity due: With an annuity due, the first payment takes place immediately.
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10. Future Value of An Ordinary Annuity
The formula for computing the future value of an ordinary annuity is:
𝑭𝑽𝑨 𝑵 = 𝑷𝑴𝑻
(𝟏+𝑰) 𝑵−𝟏
𝑰
𝐻𝑒𝑟𝑒,
𝐹𝑉𝐴 𝑁= 𝑓𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑛 𝑁 − 𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑎𝑛𝑛𝑢𝑖𝑡𝑦
𝑃𝑀𝑇 = 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑝𝑎𝑦𝑚𝑒𝑛𝑡
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11. Future Value of An Annuity Due
The future value of an annuity due is computed as follows:
𝑭𝑽𝑨 𝒅𝒖𝒆 = 𝑭𝑽𝑨 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 (𝟏 + 𝑰)
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12. Present Value of An Ordinary Annuity
The formula for computing the present value of an ordinary annuity is:
𝑷𝑽𝑨 𝑵 = 𝑷𝑴𝑻
𝟏−
𝟏
𝟏+𝑰 𝑵
𝑰
Here, PVA 𝑁 = future value of an N-period ordinary annuity
PMT = the value of the periodic payment
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13. Present Value of An Annuity Due
The present value of an annuity due is computed as follows:
𝑷𝑽𝑨 𝒅𝒖𝒆 = 𝑷𝑽𝑨 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 (𝟏 + 𝑰)
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14. Cash Flow Diagram
A cash flow diagram is a picture of a financial problem that shows all cash inflows
and outflows plotted along a horizontal time line.
Example: You are 40 years old and have accumulated $50,000 in your savings
account. You can add $100 at the end of each month to your account which pays an
annual interest rate of 6% compounded monthly. Will you be able to retire in 20
years?
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15. Benefits of The Knowledge of The TVM
For investment analysis – To decide the financial benefits of projects
To compare investment alternatives
To analyze how time impacts business activities such as loans, mortgages,
leases, savings, and annuities.
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16. Identifying TVM Problems
For a financial problem to be solved with time value of money formulas:
the periods must be of equal length
payments, if present, must all be equal and be all inflows or all outflows
payments must all occur either at the beginning or end of a period
the interest rate cannot vary along the time line
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