• The first one is into an account that is accumulating interest at an annual interest rate of 10%, compounded monthly. Using the formula for compound interest, the total after t years would be $5000(1+0.10/12)^12t.
• The second one is $250 per month, or $3000 per year. So the total in the mattress after t years would be $3000t.

We want to when our total will be $25,000; that is, we want to solve the equation

(We can't use logs to solve this since there is a plus sign between terms, and there is no rule for the log of a sum!) We solve graphically (in the exam, you must show the graph!) Graphing both sides, seeing where they intersect, and reading off the t -coordinate, we get, to three decimal places, t = 5.462 years, or about 5 years, 5 months, and 2 weeks.