If the beach house worth $350,000 had an annual value gain of 10% which is $35,000. The first year they should have $385,000, by the second year the value would of the gain would have been $38,500 which would have the house on a $423,500. By this Calculation the 3rd year gain will be $42,350 which would leave the house on a $465,850, 4th year will be gain $46,585 and worth will be$ 512,435 and that leaves us with the answer to the question on the 5th year gain will be $51,243.50 and worth will be $563,678.50
