Raymond pays $1,000 per month in rent, and he is expecting a rent increase. His landlord agreed to a gradual increase according to the following plan:
January, 0% increase
February, 5% increase
March, 10% increase from January
April, 15% increase from January
May, 20% increase from January
June, 25% increase from January.
Let matrix A be the matrix of 6 months of rent before the increase.

A = [1000 1000 1000 1000 1000 1000]

Let matrix B be the percent increase matrix with percent entries written as equivalent decimals.

Explain how AB will yield the total rent paid from January to June. What is that total?

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B = 1 1.05 1.10 1.15 1.20 1.25