I am having trouble understanding where the numbers are coming from in this question.
John and Melissa wonder about the potential increase in the value of their house. Assuming a 6% appreciation per year, the formula for the value of the house after years is 
, where starts from 0.
- Where did the 53 over 50 come from?
- Why couldn't I just calculate 6% of 219,000 for 13,140$ a year and multiply by 3 and add that to the original value?
- 53\50 is in parenthesis so I should divide that first? then apply the power of 3?
1) $$\dfrac{53}{50}=1.06=\text{6% increase or 106% of the corrent value}$$ 2) It is because for example, at $n=2$, the function calculates $6$% OF THE CURRENT VALUE, not the first value, $219000$. Eg at $n=2,$ it would increase by $6$%, to $\$232776$, then increase $6$% FROM $\$232776$ to $232776\times 1.06$
3) It does not matter,$$ \left( \frac{53^n}{50^n}\right)=(1.06)^n$$