Question

An office building rents for $40,000 the first year, then increases by 0.5% each year. Use summation notation to represent the total payments for the first three years. Explain your reasoning. Marcus’s response is given below: If rent increases by 0.5% each year, the year’s rent is 1.005 times the previous year’s rent. So, an exponential expression can be used. The summation is 1.005 raised to the year times $40,000, where the years go from 0 to 3.

Answer 1

The indices Marcus used are not correct.

As is, the indices create a summation with four terms, not three.

The upper index should be 2 instead of 3.

Explanation:

Answer 2

Given the initial rent is $40000, and the rent is increased by 0.5% each year, the rent in the third year will be given by:
FV=P(1+r)^n
FV=40000(1.05)^n
Thus the answer for the sum of payments for 3 years will be:
The summation is 1.05 raised to n years times $40000, where the years is from 0 to 3.