Compound Interest Present and Future Values Wayne Foss, MBA, MAI, CRE, Fullerton, CA USA

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

Future Value of One An Example Original Investment$1.00 Nominal Interest Rate10.0% Holding Period in Years5 Assumes Annual Compounding DollarFactor Original Investment$ Year One interest$0.10 Accumulation end of year 1$ Year Two interest$0.11 Accumulation end of year 2$ Year Three interest$0.12 Accumulation end of year 3$ Year Four interest$0.13 Accumulation end of year 4$ Year Five interest$0.15 Accumulation end of year 5$

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

Future Value of One per Period An Example

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

Sinking Fund An Example

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

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/ = Deposit $0.62 today and in five years accumulate with 10% compound interest, $1.00

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

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

Present Value of One per Period An Example

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

Level Periodic Installment An Example

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

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 10% = FW1/pd, year 10% = Sum of two factors = FW1/pd, year 2 or 2.100

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 10% = PW1, year 10% = PW1, year 10% = Sum of three factors = PW1/pd, year 3 or

So That’s Compound Interest Wayne Foss, MBA, MAI, CRE, Fullerton, CA USA