If 41 extra days are needed to complete a home, what will be the Smith Corporation's total penalty ?

Question

The Smith Homebuilding Corporation has agreed to pay a penalty for each extra das needed to build a home beyond a certain completion date. The penalty for being one day late is $32. Each day after that, the penalty is increased by $8 , and it is cumulative! If 41 extra days are needed to complete a home, what will be the Smith Corporation's total penalty ?

Answer 1

Using the formula for the sum of an arithmetic series;

S₄₁ = (41/2)[2(38) + 40(8)]