Suppose Inflation Continues at Three Percent Annually

Short Answer

Suppose inflation continues at three percent annually. (That is, an item that costs $1.00 now will cost $1.03 next year.) Let an = the value (that is, the purchasing power) of one dollar after n years.
(a) Find a recurrence relation for a_n.
(b) What is the value of $1.00 after 20 years?
(c) What is the value of $1.00 after 80 years?
(d) If inflation were to continue at ten percent annually, find the value of $1.00 after 20 years.
(e) If inflation were to continue at ten percent annually, find the value of $1.00 after 80 years.