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.
