MathIsFun

Calculating Cost

Cost in year\(_i\) is cost in year\(_{i-1}\) times 1.03

So we have:

Cost in year 1: Cost

Cost in year 2: 1.03 \(\times\) Cost

Cost in year 3: 1.03 \(\times\) 1.03 \(\times\) Cost

Cost in year 4: 1.03 \(\times\) 1.03 \(\times\) 1.03 \(\times\) Cost

\[\text{Total Cost}= \text{Cost}_1+\text{Cost}_2+\text{Cost}_3+\text{Cost}_4\\ =\text{Cost}\times(1+1.03+1.03^2+1.03^3)\\ =\text{Cost}\times(1.03^0+1.03+1.03^2+1.03^3)\\ =\text{Cost}\times\sum_{i=0}^{3}1.03^i\\ =\text{Cost}\times\frac{1.03^4-1}{1.03-1}\] =Cost \(\times\) 4.183627