We use cookies to enhance your experience on our website. By continuing to use our website, you are agreeing to our use of cookies. You can change your cookie settings at any time. Find out more  ### More Interest Formulas

Go to questions covering topic below

Suppose that there is a series of "n" payments uniformly spaced but differing from one period to the next by a constant. The change or "gradient" from one period to the next is denoted "G." Let A1 be the payment at EOY 1.

EOY = End of year

NCF = Net Cash Flow

Example 1:

 EOY NCF (\$) 1 100 2 150 3 200 4 250 To find the Present Worth, at EOY 0, of a gradient series that begins EOY 1, use

A1 = \$100; G = + \$50; i = 7%

P = A1 (P/A,i%,n) + G (P/G,i%,n)

Note that you must subtract the annual amount, A1, 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:

 EOY NCF (\$) 1 100 2 90 3 80 4 70 To find the annual equivalent (A series) of a gradient series that begins EOY 1, use

A1 = 100; G = - \$10; i = 10%

A = A1 + G (A/G,i%,n)

A = 100 - 10 (A/G, 10%, 4)

A = 100 - 10 (1.388 )

A = \$86.12

Now, find the present value at 10% interest of the series of payments given in Example 2 above.

P = \$100 (P/A,10%,4) + ( - \$10) (P/G,10%,4)

= \$100 (3.170) - \$10 (4.378) = \$273

### More Interest Formulas

Question 1

Question 2

Question 1.

Using an interest table gradient series factor, write an equation to find the Present Worth (at EOY 0) of the following series of payments. Interest is 5%.

 EOY NCF (\$) 0 -1,000 1 500 2 600 3 700 4 800 5 900

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A P = - 1,000 + 500 (P/G,5%,5)

B P = - 1,000 + 500 (P/A,5%,5) + 100 (P/G,5%,5)

C P = - 1,000 + 500 (P/A,5%,5) + 100 (P/G,5%,4)

D P = - 1,000 + 500 (P/F,5%,1) + 100 (P/G,5%,5)

Review topic

Question 2.

Using an interest table gradient series factor, write an equation to find the Present Worth (at EOY 0) of the following series of payments. Interest is 7%.

 EOY NCF (\$) 0 -1,000 1 0 2 0 3 400 4 800 5 1200

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A P = - 1,000 + 400 (P/G,7%,4) (P/F,7%,1)

B P = - 1,000 + 400 (P/G,7%,4)

C P = - 1,000 + 400 (P/A,7%,3) + 400 (P/G,7%,3)

D P = - 1,000 + 400 (P/G,7%,3) (P/F,7%,2)

Review topic 