## Uniform gradient future worth formula

Use uniform series and gradient factors when cash flows are shifted. 5. The formulas relate a present worth P or a future worth F to a uniform series amount A . formula for the present worth of a perpetual geometric gradient. Though may help practitioners and students develop a feel for the economics of long-lived  Engineering Economics Made Easy - Step by Step - with the TI-Nspire CX (CAS) ◁ Future Value Uniform Annual Series and Present Value, Arithmetic Gradient Income Tax Calculation; Compute any Rate [%] by Definition; Present Value

Arithmetic Gradient Factors (P/G, A/G) amount are considered arithmetic gradient cash flows. To find the uniform annual series, A, for an arithmetic gradient  understanding of engineering economics. For most A mathematical formula for Simple Interest can be written as: = ×. × Uniform gradient future worth. G to F. Use uniform series and gradient factors when cash flows are shifted. 5. The formulas relate a present worth P or a future worth F to a uniform series amount A . formula for the present worth of a perpetual geometric gradient. Though may help practitioners and students develop a feel for the economics of long-lived  Engineering Economics Made Easy - Step by Step - with the TI-Nspire CX (CAS) ◁ Future Value Uniform Annual Series and Present Value, Arithmetic Gradient Income Tax Calculation; Compute any Rate [%] by Definition; Present Value  For example we could find the equivalent future value F of a present amount P payments A. Equation of Value is obtained by setting the sum of the values on a n years Uniform Gradient Amount (G) – Uniform Gradient Amount that repeats  The formula for the future value of a growing annuity is used to calculate the future amount of a series of cash flows, or payments, that grow at a proportionate

## The uniform gradient present worth, UGPW, is a Discrete Compounding Discount factor. This discount factor is used to calculate the present worth of the future value of a cash flow changing by a uniform gradient. Present value = Future value * discount factor.

Choose ONE formula from the following list Uniform Gradient Future Worth. Uniform Gradient Uniform Series, Simple Interest Rate. Effective Interest Rate More Interest Formulas. Uniform annual series and future value. Go to questions covering topic below. Suppose that there is a series of "n" uniform payments,  Uniform Annual Series and Future Value More Interest Formulas Suppose that there is a series of "n" payments uniformly spaced but differing from one To find the Present Worth, at EOY 0, of a gradient series that begins EOY 1, use. Future Worth (F): equivalent future amount at t = n of any present amount at Uniform Gradient Amount (G): uniform gradient amount that repeats at the end of NOTE: The answers arrived at using the formula versus the factor table turn out to  A single payment at some time in the future. A uniform annual payment over several years. For example, consider a lottery that is held in a fictional state  Name Compound Amount Single Payment P given F Present Worth Uniform Gradient Present Worth Uniform Gradient T Uniform Gradient Uniform Series Net P me The formula for dis d-it f (ixD at time 114 ENGINEERING ECONOMICS   analysis to evaluate present and future worth receipts and disbursements of series present worth formula is used to calculate the present worth of the uniform

### The formula for the future value of a growing annuity is used to calculate the future amount of a series of cash flows, or payments, that grow at a proportionate

where P A is the present worth of the uniform series only, P G is the present worth of the gradient series only, and the + or - sign is used for an increasing ( +G ) or decreasing ( -G ) gradient, respectively. Engineering Economics (in years) Enter a value for F,P,A,or G here: Choose ONE formula from the following list . Single Payment Compound Amount: Single Payment Present Worth: Uniform Series Sinking Fund: Capital Recovery: Uniform Series Compound Amount: Uniform Series Present Worth: Uniform Gradient Present Worth: Uniform Gradient Future Worth: Engineering Economics 4-2c Discount Factors and Equivalence Example (FEIM): What factor will convert a gradient cash flow ending at t = 8 to a future value? The effective interest rate is 10%. The F/G conversion is not given in the factor table. However, there are different ways to get the factor using the factors that are in the table. For example, The general equation to find the present worth of an arithmetic gradient cash flow series is: P = present worth of base amount + present worth of gradient amount = A (P/A,i,n) + G (P/G, i,n) Uniform Gradient Present Worth Uniform Gradient † Future Worth to F given G (F/G, i%, n) i n i i n computing present worth values P and Net P. The formula for d is d = i + f + ( × f) ENGINEERING ECONOMICS 115 DEPRECIATION Straight Line D n CS j = - n Accelerated Cost Recovery System (ACRS) Future Worth of a Uniform Series of Amounts Year Interest during year Amount at end of year. 1 0 R 2 Ri R + Ri + R = R[(1 + i) + 1] 3 R[(1 + i) + 1]i R[(1 + i) + 1] + R[(1 + i) + 1]i + R = R[(1 + i)2 + (1+i) + 1] The discount formula can be written as P=F*(P/F,i%,n), where (P/F,i%,n) is the symbol used to define the discount factor. To convert the future value to the equivalent present value, you simply multiple the future value by the discount factor.

### The uniform gradient present worth, UGPW, is a Discrete Compounding Discount factor. This discount factor is used to calculate the present worth of the future value of a cash flow changing by a uniform gradient. Present value = Future value * discount factor.

Uniform annual series and future value. Question 1. Question 2. Return to Uniform annual series and future value Return to More Interest Formulas Tutorials menu. Return to Tutorials menu. Question 1. Suppose that \$1,000 is invested quarterly at 6% interest, compounded quarterly. How much will be in the account after five years? The uniform gradient present worth, UGPW, is a Discrete Compounding Discount factor. This discount factor is used to calculate the present worth of the future value of a cash flow changing by a uniform gradient. Present value = Future value * discount factor. single payment present worth: uniform gradient future worth: uniform gradient present worth: uniform gradient uniform series: uniform series compound amount: uniform series present worth: uniform series sinking fund: References - Books: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition. To find the Present Worth, at EOY 0, of a gradient series that begins EOY 1, use. A 1 = \$100; G = + \$50; i = 7%. P = A 1 (P/A,i%,n) + G (P/G,i%,n) Note that you must subtract the annual amount, A 1, from all annual amounts before applying the gradient factor. P = 100 (P/A,7%, 4) + 50 (P/G, 7%, 4) P = 100 (3.387) + 50 (4.795) P = 578.45. Example 2: The term in the brackets is called the arithmetic-gradient uniform-series factor. To compute a future amount from a linear gradient series use: The term in the brackets is called the arithmetic-gradient series future worth factor. The general equations for calculating total present worth are PT = PA + PG and PT = PA - PG.

## Figure 1-7: Uniform Series Present-Worth Factor, P/Ai,n Equation 1-5 gives the cumulated present value, P, of all uniform series of equal investments, A, to receiving the end of the period payments equals the summation of future values:.

The formula for the Uniform Gradient Future Worth (UGFW) is: UGFW = ( (1+i)^n - 1)/(i^2) - n/i) where: UGFW is the Uniform Gradient Future Worth (UGFW) n is the number of periods; i is the interest rate per period. EXAMPLE: If the inputs are: n = 20 periods of uniformly increasing cash flows; i = 4.7 % ; The UGFW is approximately: 256.10, which can be used to convert a gradient cash flow into a future value. REFERENCE. Lindeburg, Michael R (1992). Uniform annual series and future value. Question 1. Question 2. Return to Uniform annual series and future value Return to More Interest Formulas Tutorials menu. Return to Tutorials menu. Question 1. Suppose that \$1,000 is invested quarterly at 6% interest, compounded quarterly. How much will be in the account after five years? The uniform gradient present worth, UGPW, is a Discrete Compounding Discount factor. This discount factor is used to calculate the present worth of the future value of a cash flow changing by a uniform gradient. Present value = Future value * discount factor. single payment present worth: uniform gradient future worth: uniform gradient present worth: uniform gradient uniform series: uniform series compound amount: uniform series present worth: uniform series sinking fund: References - Books: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.

To find the Present Worth, at EOY 0, of a gradient series that begins EOY 1, use. A 1 = \$100; G = + \$50; i = 7%. P = A 1 (P/A,i%,n) + G (P/G,i%,n) Note that you must subtract the annual amount, A 1, from all annual amounts before applying the gradient factor. P = 100 (P/A,7%, 4) + 50 (P/G, 7%, 4) P = 100 (3.387) + 50 (4.795) P = 578.45. Example 2: The term in the brackets is called the arithmetic-gradient uniform-series factor. To compute a future amount from a linear gradient series use: The term in the brackets is called the arithmetic-gradient series future worth factor. The general equations for calculating total present worth are PT = PA + PG and PT = PA - PG. where P A is the present worth of the uniform series only, P G is the present worth of the gradient series only, and the + or - sign is used for an increasing ( +G ) or decreasing ( -G ) gradient, respectively. Engineering Economics (in years) Enter a value for F,P,A,or G here: Choose ONE formula from the following list . Single Payment Compound Amount: Single Payment Present Worth: Uniform Series Sinking Fund: Capital Recovery: Uniform Series Compound Amount: Uniform Series Present Worth: Uniform Gradient Present Worth: Uniform Gradient Future Worth: Engineering Economics 4-2c Discount Factors and Equivalence Example (FEIM): What factor will convert a gradient cash flow ending at t = 8 to a future value? The effective interest rate is 10%. The F/G conversion is not given in the factor table. However, there are different ways to get the factor using the factors that are in the table. For example,