time money
TRANSCRIPT
Time Value of money concepts:
The time value of money means that money can be invested today to earn interest and grow to a larger dollar amount in the future. Time value of money concepts is useful in valuing several assets and liabilities. Interest is the amount of money paid or received in excess of the amount borrowed or lent.
Simple Interest:
Simple Interest Example:
Simple Interest (FV):
Part I
Compound interest includes interest not only on the initial investment but also on the accumulated interest in previous periods.
Assume we deposit $1,000 in a bank that earns 6% interest compounded annually. What is the balance in our account at the end of three years?
Part II
Each year we earn interest on the initial investment amount plus any previously earned interest. As a result, at the end of the three years, we have a total of $1,191.02.
After 1 year:
FV1 = PV + PV (i)
= PV(1 + i)
= $100(1.10)
= $110.00
After 2 years:
FV2 = FV1(1+i) = PV(1 + i)(1+i)
= PV(1+i)2
= $100(1.10)2
= $121.00
After 3 years:
FV3 = FV2(1+i)=PV(1 + i)2(1+i)
= PV(1+i)3
= $100(1.10)3
= $133.10
In general,
FVN = PV(1 + i)N
Compound Interest (PV)Present Value of a Single Amount:
Instead of asking what is the future value of a current amount, we might want to know what amount we must invest today to accumulate a known future amount.
This is a present value question.
Present value of a single amount is today’s equivalent to a particular amount in the future.
Present Value of a Single Amount:
Using our previous equation for future value, we can solve for present value by dividing the future value by 1 plus the interest rate raised to the number of periods. Another way to solve for the present value is to use the Present Value of $1 table in your textbook. In your textbook, Table 2 is the Present Value of $1 table. Does the format look familiar?
Present Value of a Single Amount:
Assume you plan to buy a new car in 5 years and you think it will cost $20,000 at that time.
What amount must you invest today in order to accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually?
Present Value of a Single Amount:
To solve this question, we multiply the future value of $20,000 by the present value factor for 8% for 5 periods which is .68058.
If you deposit $13,611.60 now, at 8% annual interest, you will have $20,000 at the end of 5 years.
Solving for Other Values:
There are four variables needed when determining the time value of money. If you know any three of these, the fourth can be determined by using a little algebra.
Double Your Money!
