Suppose Inflation Continues at Three Percent Annually

question 18

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.

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Definitions:

Equivalent

A term used to denote items, quantities, or expressions that have the same value or function, even though they may appear different at first glance.

Canada Savings Bonds

Canadian government savings products that are available for a limited period each year and offer a guaranteed rate of interest.

Per Annum

A term used to represent an annual occurrence or an amount over the course of a year.

Cashing In

The process of selling or converting a financial asset or investment for cash.