The rate of inflation is 3%. The cost of an item in future years can be found by iterating the function c(x) = 1.03x. Find the cost of a $1500 refigerator in th

Question

The rate of inflation is 3%. The cost of an item in future years can be found by iterating the function c(x) = 1.03x. Find the cost of a $1500 refigerator in three years if the rate of inflation remains consistant.

Answer 1

For a geometric sequence:

 

a_n = a₁(r)^n-1, where a₁ = initial amount, r = common ratio, n = number of terms

 

a₃ = 1500(1.03)^3-1

a₃ = 1500(1.03)²

a₃ = 1500(1.0609)

a₃ = 1591.35

 

In three years the item shall cost $1,591.35.