# Time Value Of Money

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The time value of money is a way to calculate the value of a sum of money in the present or in the future. It allows the calculation of Present Value, which is the present value of an amount that is received in the future. It also can calculate Future Value, which is the future worth of a present amount. Also included is the Present Value of an Annuity, which is the present value of a stream of future payments. It can determine the value of your mortgage today, if you can afford 20 years of payments of \$X. Another calculation is Future Value of an Annuity, which is the future value of a stream of payments (annuity).

The premise of time value of money is that an investor prefers to receive money today, rather than the same amount in the future, all else being equal. As a result, the investor demands interest to compensate, which may be paid periodically or at the end of the period. The interest compensates for the time in which the money could be put to productive use, the risk of default, and the risk of inflation.

Earning interest on interest is called compounding or compound interest. If the interest is higher then the faster your money will grow if left in a savings account. (Brealy, Myers, Marcus, 2003) There is a famous example of the power of compound interest, which is the sale of Manhattan Island. (p.70). Peter Minuit bought the island in 1626 for \$24. Based on real estate values in New York today, this was an amazing deal. \$24 invested for 377 years at an 8% interest rate is around \$95 trillion. Compound growth means that value increases each period by factor. When money is invested in at compound interest, the growth is in the interest rate. (p.71).

An annuity is another factor when looking at the Time Value of Money. An annuity is an equally spaced level stream of cash flows with a finite maturity. If the cash flow stream is infinite then, it is a perpetuity.

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