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

## Presentation on theme: "Compound Interest Present and Future Values Wayne Foss, MBA, MAI, CRE, Fullerton, CA USA"— Presentation transcript:

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

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\$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

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 1/1.610151 = 0.62092 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 1 @ 10% = 1.100 FW1/pd, year 1 @ 10% = 1.000 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 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

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

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

Similar presentations