You deposit 2000 in account a, which pays 2.25% annual interest compounded monthly. you deposit another 2000 in account b, which pays 3% annual interest compounded monthly. when is the sum of the balance in both accounts at least 5000

To model this situation, we are going to use the compound interest formula: 
where
is the final amount after  years 
is the initial deposit 
is the interest rate in decimal form 
is the number of times the interest is compounded per year
is the time in years 

For account A: 
We know for our problem that  and . Since the interest is compounded monthly, it is compounded 12 times per year; therefore, . Lets replace those values in our formula:


For account B:
, , . Lest replace those values in our formula:


Since we want to find the time, , when  the sum of the balance in both accounts is at least 5000, we need to add both accounts and set that sum equal to 5000:


Now that we have our equation, we just need to solve for :









We can conclude that after 17.47 years the sum of the balance in both accounts will be at least 5000.