At the end of each month for 20 years, you deposit $150 into a savings plan. you then make no further deposits, but leave the money in the plan for another 10 years. if the plan earn 5.5% compounded monthly, what will the balance be at the end of the 30-year period?

The balance resulting from 20 years' payments into the plan is the sum of a geometric series with first term $150 and common ratio 1+.055/12 (the monthly balance increase). That balance is
.. $550*((1 +.055/12)^240 -1)/(.055/12) ≈ $239,595.07

This balance is increased by the factor (1 +.055/12) each month for 120 months, so it is multiplied by (1 +.055/12)^120 over the 10 years.
.. $239,595.07*(1 +.055/12)^120 = $414,757.38

At the end of the 30-year period, the balance will be $414,757.38.