Introduction and Basic Time Value of Money Formula - (TVM)
Time Value of Money
The time value of money refers to that there are greater benefits to receive money sooner than later.
Money that you have in hand today can be invested in earn a positive rate of return, producing more money in tomorrow. Because of that, a dollar is worth more than a dollar in the future.
- What are the present value and future value of something?
Time value of money considers two values of time.These are-
1) Present Value of Money (PV)
2)Future Value of Money (FV)
Key points of TVM
Time Line: A graphical representation of a period of time.
Future Value: Future Value refers how much the present value of cash or assets that will be worth in the future at a specific date.
Compound Interest: Compound interest is an interest that is earned on a given deposit.It has become part of the principle at the end of a specified period.
Principal: Principal is the amount of money on which interest is paid.
Present Value: Present value is the current dollar value of a future amount.It is the amount of money that would have to be invested today at a given interest rate over a specified period to equal the future amount.
Discounting Cash Flows: Discounting cash flows is the process of finding present values.It is the inverse of compounding interest.
Perpetuity: Perpetuity is the bond or other security which has no fixed maturity date.
Mixed Stream: In a mixed stream, there is no particular cash flows pattern and It is a stream of unequal periodic cash flows.
Semiannual Compounding: It is the compounding of interest over 2 periods within the year.
Quarterly Compounding: It is the compounding of interest over four periods within the year.
Formula of Basic Time Value of Money
The TVM formula may change based on the exact situation in question.
Formula
Time Value of Money
The time value of money refers to that there are greater benefits to receive money sooner than later.
Money that you have in hand today can be invested in earn a positive rate of return, producing more money in tomorrow. Because of that, a dollar is worth more than a dollar in the future.
- What are the present value and future value of something?
Time value of money considers two values of time.These are-
1) Present Value of Money (PV)
2)Future Value of Money (FV)
Key points of TVM
Time Line: A graphical representation of a period of time.
Future Value: Future Value refers how much the present value of cash or assets that will be worth in the future at a specific date.
Compound Interest: Compound interest is an interest that is earned on a given deposit.It has become part of the principle at the end of a specified period.
Principal: Principal is the amount of money on which interest is paid.
Present Value: Present value is the current dollar value of a future amount.It is the amount of money that would have to be invested today at a given interest rate over a specified period to equal the future amount.
Discounting Cash Flows: Discounting cash flows is the process of finding present values.It is the inverse of compounding interest.
Perpetuity: Perpetuity is the bond or other security which has no fixed maturity date.
Mixed Stream: In a mixed stream, there is no particular cash flows pattern and It is a stream of unequal periodic cash flows.
Semiannual Compounding: It is the compounding of interest over 2 periods within the year.
Quarterly Compounding: It is the compounding of interest over four periods within the year.
Time Line: A graphical representation of a period of time.
Future Value: Future Value refers how much the present value of cash or assets that will be worth in the future at a specific date.
Compound Interest: Compound interest is an interest that is earned on a given deposit.It has become part of the principle at the end of a specified period.
Principal: Principal is the amount of money on which interest is paid.
Present Value: Present value is the current dollar value of a future amount.It is the amount of money that would have to be invested today at a given interest rate over a specified period to equal the future amount.
Discounting Cash Flows: Discounting cash flows is the process of finding present values.It is the inverse of compounding interest.
Perpetuity: Perpetuity is the bond or other security which has no fixed maturity date.
Mixed Stream: In a mixed stream, there is no particular cash flows pattern and It is a stream of unequal periodic cash flows.
Semiannual Compounding: It is the compounding of interest over 2 periods within the year.
Quarterly Compounding: It is the compounding of interest over four periods within the year.
Formula of Basic Time Value of Money
The TVM formula may change based on the exact situation in question.
In case of Fixed Deposits-
Where,
Where,
FV= Future Value of Money
PV= Present Value of Money
i = Interest Rate
n= Number of years
m= Number of compounding in a year
m= Number of compounding in a year
The value of "m"
When,
Compounding Annually or Yearly...Then m=1
Compounding Half yearly or Semi-Annually...Then m=2
Compounding Quarterly...Then m=4
Compounding Monthly...Then m=12
Compounding Daily...Then m = 365
# A sum of $10,000 is invested for 1 year at 10 percent interest rate.Calculate the future value of that money.
Solution-
Given that,
PV=$10,000
n = 1 year
i = 10% or 0.1
FV=?
Now, FV=PV(1+i)n
= $10,000(1+0.1)1
= 10,000(1.1)
=$11000
Hence, the future value of that money is $11,000.
#The value of $5,000 one year from today, compounded at 7% interest.Calculate the value.
Solution:
Given that,
FV=$5000
n=1 year
i = 7% or 0.07
PV= ?
Now, FV=PV(1+i)n
=>5000=PV(1+0.07)1
=>5000=PV(1.07)
=>PV=5000/1.07
=4672.9
Hence, The present value is $4672.9
Effect of Compounding Periods on Future Value
The number of compounding periods can have a drastic effect on the TVM calculations.
The number of compounding periods can have a drastic effect on the TVM calculations.
#Assume, You have $10,000 to invest today at 7% interest compounded (Annually/Semi-Annually/Quarterly/Monthly/Daily).
Find how much you will have accumulated in the account at the end of 3 years.
Solution:
In case of compounding annually
Given that,
PV=$10,000
i =7% or 0.07
n=3 years
m=1
FV= ?
Now, FV=PV(1+i/m)mn
=$10,000(1+0.07/1)1*3
=10,000(1+0.07)3
=10,000(1.07)3
=10,000(1.225)
=$12,250
Hence, the future value is $12,250
Note: No need to solve by using the formula with "m" when compounded Annually.Because the value of m is 1 when the invest compounding annually.
In case of compounding Semi-Annually
Given that,
PV=$10,000
i =7% or 0.07
n=3 years
m=2
FV= ?
Now, FV=PV(1+i/m)mn
=$10,000(1+0.07/2)2*3
=10,000(1+0.035)6
=10,000(1.035)6
=10,000(1.229)
=$12,290
Hence, the future value is $12,290
Now Calculate FV in case of Quarterly, Monthly, Daily by following the formula.
Put,
m=4...in case of Quarterly Compounding
m=12...in case of Monthly Compounding
m=365...in case of Daily Compounding
From above of the discussion, we can say that Time Value of money is not only on interest rate and time horizon but how many times the compounding calculations are computed each year.
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