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The Time Value of Money
The Time Value of Money is the concept that a dollar today is
worth more than a dollar in the future. The reason for this is
that you could invest a dollar today and receive interest on that dollar
in the future. The interest is your compensation for not being
able to spend that dollar yourself. The longer into the future
that dollar stays invested, the more interest it will earn.
The Time Value of Money concept is fundamental to the structuring and
sale of cash flows.
Definitions
Interest:
Interest is the cost of borrowing money, usually represented as a
percentage rate.
Periods:
Periods are evenly-spaced periods of time corresponding to the
compounding of interest (e.g. daily, monthly, semi-annually, annually).
In other words, at each period, an additional interest charge will be
applied.
Payments:
Payments are a series of evenly-spaced cash-flows that are transfers of
money (in either direction) between the parties involved in an
investment.
Present Value:
Present Value is an amount today that is equivalent to a future
payment, or series of payments, that is discounted by an appropriate
compounded interest rate.
Future Value:
Future Value is the amount of money that an investment with a fixed, compounded
interest rate will grow to by some future date.
Loan Amortization:
A schedule for repaying a loan in equal installments. A portion of
each payment is applied to interest charges and the remainder is applied
to the outstanding principal balance. As the principal balance is
reduced, the interest charges will also be reduced and a larger portion
of each payment will apply to further principal reduction.
Examples:
| Time |
Value1 |
Value2 |
| Initial Investment |
$1,000.00 |
$783.53 |
| Year 1 |
$1,050.00 |
$822.70 |
| Year 2 |
$1,102.50 |
$863.84 |
| Year 3 |
$1,157.63 |
$907.03 |
| Year 4 |
$1,215.51 |
$952.38 |
| Year 5 |
$1,276.28 |
$1,000.00 |
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If you have $1000 and invest it at an annual compounded interest
rate of 5%, your investment would grow according to the Value1
column of the above table:
So, the Future Value of this investment in five years is $1,276.28.
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Conversely, suppose someone asks you for a loan now and they can
give you back exactly $1,000 in five years, and you want to make 5%
interest on your money.
Using the Value2 column in the above table, you can see that
the Present Value (i.e. what you should loan now) is $783.53.
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