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Compound Interest Present and Future Values Wayne Foss, MBA, MAI, CRE, Fullerton, CA USA Email: waynefoss@usa.net

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Future Value of One n Also known as the FW of 1 n Formula: S n = (1 + i) n n Where: S n = Future Factor i = effective rate of interest n = number of compounding periods

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Future Value of One An Example Original Investment$1.00 Nominal Interest Rate10.0% Holding Period in Years5 Assumes Annual Compounding DollarFactor Original Investment$1.001.0000 Year One interest$0.10 Accumulation end of year 1$1.10 1.1000 Year Two interest$0.11 Accumulation end of year 2$1.21 1.2100 Year Three interest$0.12 Accumulation end of year 3$1.33 1.3310 Year Four interest$0.13 Accumulation end of year 4$1.46 1.4641 Year Five interest$0.15 Accumulation end of year 5$1.61 1.61051

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Future Value of One per Period n Also known as the FW of 1/Pd – The total accumulation of principal and interest of a series of deposits. n Formula: S n = (S n - 1)/i n Where: S n = Future Factor i = effective rate of interest n = number of compounding periods

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Future Value of One per Period An Example

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Sinking Fund Factor n The level periodic payment or investment required to accumulate one in a given number of periods including the accumulation of interest. n Formula: 1/S n = i/(S n - 1) n Where: S n = Future Factor of one i = effective rate of interest n = number of compounding periods

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Sinking Fund An Example

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Present Value of One n Also known as the PW of 1 n Formula: 1 / S n = 1 / (1 + i) n n Where: S n = Future Factor i = effective rate of interest n = number of compounding periods

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Present Value of One An Example Future Investment$1.00 Nominal Interest Rate10.0% Holding Period in Years5 Assumes Annual Compounding One (1) divided by the five (5) year future value factor equals the required deposit to accumulate $1.00 in five (5) years or 1/1.610151 = 0.62092 Deposit $0.62 today and in five years accumulate with 10% compound interest, $1.00

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Present Value of One per Period n Also known as the PW of 1/pd n Formula: a n = (1 - 1/S n ) / i Where: a n = Level Annuity Factor 1/S n = Present Value Factor i = effective rate of interest n = number of compounding periods

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Present Value of One per Period An Example n Can be calculated as a series of single reversions (Present Value of 1) n Can use a table of factors to calculate n Can use a financial calculator to calculate the value, or extract a factor

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Present Value of One per Period An Example

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Level Periodic Installment n Also known as the Installment Factor n Formula: 1/a n = i/(1 - 1/S n ) Where: 1/a n = Installment Factor 1/S n = Present Value 1 per period Factor i = effective rate of interest n = number of compounding periods

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Level Periodic Installment An Example

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Relationships n Future Worth of One is the reciprocal of the Present Worth of One n Amortization Factor is the reciprocal of the Present Worth of One per Period n Sinking Fund Factor is the reciprocal of the Future Worth of One per Period

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Relationships n Any Future Worth of 1 per Period can be derived by adding the future worth of one factor for the preceding year to the same year factor for the future worth of one per period factor. – Example: FW1, year 1 @ 10% = 1.100 FW1/pd, year 1 @ 10% = 1.000 Sum of two factors = FW1/pd, year 2 or 2.100

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Relationships n Any Present Worth of 1 per Period can be derived by adding the present worth of one factor for the number of years factor that is desired. – Example: PW1, year 1 @ 10% = 0.909091 PW1, year 2 @ 10% = 0.826446 PW1, year 3 @ 10% = 0.751315 Sum of three factors = PW1/pd, year 3 or 2.486852

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So That’s Compound Interest Wayne Foss, MBA, MAI, CRE, Fullerton, CA USA Email: waynefoss@usa.net

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Learning Goals Discuss the role of time value in finance and the use of computational aids to simplify its application. Understand the concept of future.

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