Arithmetic Gradient

• The first cash flow is always equal to zero.
• A uniform increasing amount. 
• G = the difference between each cash amount.

A pure gradient (uniformly increasing amount) can also be converted into the equivalent present value of uniform series:

AG = G(A/G, i, n)

Example: The list price for a vehicle is stated as $25,000.  You are quoted a monthly payment of $658.25 per month for 4 years.  What is the monthly interest rate?  What interest rate would be quoted (yearly interest rate)?

Using factor table:

$25000 = $658.25(P/A,i,48)

 37.974 = (P/A,i,48)

 i = 1% from table 4, pg 705

 0r 12 % annually

Using formula:

Example: Find the number of periods required such that an invest of $1000 at 5% has a future worth of $5000.

  $P = $F(P/F,5%,n)

  $1000 = $5000(P/F,5%,n)

   .2 = (P/F,5%,n)

   n ~ 33 periods