Uniform Gradient Uniform Series (UGUS)

The Uniform Gradient Uniform Series (UGUS) factor calculator computes the change in the amount of an account that has uniform increases or decreases applied to it for some number of compounding periods.

INSTRUCTIONS:  Choose units and enter the following:

• (i) Interest Rate per Period
• (n) Number of periods

Uniform Gradient Uniform Series factor (UGUS):  The calculator returns the factor.

The Math / Science

The formula for the Uniform Gradient Uniform Series (UGUS) factor is:

  `UGUS= 1/i -n/((1+i)^n-1)`

where:

• UGUS is the uniform gradient uniform series factor.
• i is the interest rate per period
• n is the number of periods.

 This basically computes the change in the amount of an account that has uniform increases or decreases applied to it for some number of compounding periods.

EXAMPLES

In a uniform gradient cash flow the cash flow changes by the same amount in each payment period. For example, if the cash flow in period 1 is $2000, and in period two it is $2100 it would be a uniform gradient if the subsequent amounts increased by $100 in each subsequent period. This gradient in this example would be equal to $100.

If the cash flow in this increasing gradient example continued to increase for 20 periods, with a fixed interest rate of 4.5 %, then:

• N = 20
• i = 4.5

and the factor of UGUS increase would be calculated to be approximately: 8.055 annual increase.

If the gradient were negative, and the cash flows were diminishing uniformly by the same amount each period, the change factor would be a negative factor of approximately -8.055.

NOTES

The Uniform Gradient Uniform Series (UGUS) is a Discrete Compounding Discount Factor.  It could also be referred to as the Arithmetic Gradient to Uniform Series Factor.

This equation takes an arithmetic gradient series and converts it to a uniform series. The two series have the same number of cash flow periods.  The first cash flow of the gradient series is 0.

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Present and Future Worth Calculators

• (SPCA) Single Payment Compound Amount Factor
• (USSF) Uniform Series Sinking Fund Factor 
• (SPPW) Single Payment Present Worth Factor
• (UGFW) Uniform Gradient Future Worth Factor 
• (UGPW) Uniform Gradient Present Worth Factor 
• (UGUS) Uniform Gradient Uniform Series Factor 
• (USCA) Uniform Series Compound Amount Factor 
• (USPW) Uniform Series Present Worth Factor 

REFERENCE

• Lindeburg, Michael R (1992). Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.