Suppose Inflation at Three Precent Annually

Suppose inflation at three precent annually. (That is , an item that costs $q.00 now will costs $1.03 next year.) ley 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 .