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# SSNT6_DCF - Time Value of Money Concepts Definitions Time...

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Time Value of Money Concepts

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Definitions Time value of money – Money can be invested today to earn interest and grow to a larger dollar amount in the future Interest – The rent paid for the use of money for some period of time. In dollar terms, it is the amount of money paid or received in excess of the amount of money borrowed or lent
Simple Interest Interest amount = P i n Assume you invest \$1,000 at 6% simple interest for 3 years. You would earn \$180 interest. (\$1,000 .06 3 = \$180) ( or \$60 each year for 3 years )

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Definition Compound interest – includes interest not only on the initial investment but also on the accumulated interest in previous periods Example: – Tim Tebow invested \$1,000 in a savings account paying 6% interest compounded annually
Compound Interest Original balance 1,000.00 \$ First year interest 60.00 Balance, end of year 1 1,060.00 \$ Balance, beginning of year 2 1,060.00 \$ Second year interest 63.60 Balance, end of year 2 1,123.60 \$ Balance, beginning of year 3 1,123.60 \$ Third year interest 67.42 Balance, end of year 3 1,191.02 \$

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Future Value of a Single Amount The future value of a single amount is the amount of money that a dollar will grow to at some point in the future. Assume we deposit \$1,000 for three years that earns 6% interest compounded annually. \$1,000.00 1.06 = \$1,060.00 and \$1,060.00 1.06 = \$1,123.60 and \$1,123.60 1.06 = \$1,191.02
Future Value of a Single Amount: Using an Equation FV = PV (1 + i) n where: PV = Amount invested at the beginning of the period FV = Future value of the invested amount i = Interest rate n = Number of periods FV = \$1,000 * (1 + 0.06) 3 = \$1,191.02

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Future Value of a Single Amount: Using a Table Using the Future Value of \$1 Table, we find the factor for 6% and 3 periods is 1.19102. FV = \$1,000 1.19102 = \$1,191.02 Interest Rates ( i ) 6% 7% 8% 9% 10% 11% Periods ( n ) 1 1.06000 1.07000 1.08000 1.09000 1.10000 1.11000 2 1.12360 1.14490 1.16640 1.18810 1.21000 1.23210 3 1.19102 1.22504 1.25971 1.29503 1.33100 1.36763 4 1.26248 1.31080 1.36049 1.41158 1.46410 1.51807 5 1.33823 1.40255 1.46933 1.53862 1.61051 1.68506
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

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Present Value of a Single Amount Remember our equation? FV = PV (1 + i) n We can solve for PV and get . . . . FV (1 + i ) n PV =
Present Value of a Single Amount PV = \$1331 / (1 + 0.06) 3 = \$1,331 / 1.19102 = \$1,000 FV (1 + i ) n PV =

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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 i = .08, n = 5 Present Value Factor = .68058 (from Table) \$20,000 .68058 = \$13,611.60 If you deposit \$13,611.60 now, at 8% annual interest, you will have \$20,000 at the end of 5 years.

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Solving for Other Values FV = PV (1 + i ) n Future Value Present Value Interest Rate Number of Compounding Periods There are four variables needed when determining the time value of money.
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SSNT6_DCF - Time Value of Money Concepts Definitions Time...

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