Your cat just won the local feline lottery to the tune of 30

Your cat just won the local feline lottery to the tune of 3000 cans of \"9-Lives\" cat food (assorted flavors). A local grocer offers to take the 3000 cans and in return, supply 30 cans a month for the next 10 years. What rate of return, in terms of nominal annual rate, will you realize on this deal? (Compute to the nearest 0.01%).

Solution

P = 3000

A = 30

i = ?

n = 120 (i.e. 10*12)

P = A(P/A, i, n)

3000 = 30(P/A, i, 120)

=> (P/A, i, 120) = 3000/30 = 100

Using trial and error:

Let i = 0.25%

(P/A, 0.25%, 120) = 103.563

Let i = 0.5%

(P/A, 0.5%, 120) = 90.074

By using interpolation method:

i = 0.25% +[(103.563 - 100)/ (103.563 - 90.074)] * (0.5% - 0.25%)

= 0.0025 + 0.264(0.0025)

= 0.00316 (per month)

Nominal Annual Rate = 12 * 0.00316 = 0.0379    or 3.79%