Compound Interest - Intuition is wrong
I need some help regarding an alternate approach to the following problem.
In 1960 a man earned $2,000 and spent it all. During the next 10 years his salary increased by 5% per annum(compound interest), but inflation caused his expenditure to rise by 4% per annum(compound interest). Find how much he had saved by the end of 1970, giving your answer to two significant figures.
My intuition tells me that +5%(income) and -4%(expense) should given a +1% increase compound annually on the initial amount. So I used the formula for the Sum at nth year for compound interest with
But this approach gives an incorrect answer.
However if I break down the problem separately, Using for Income, and for Expenses. I get,
The answer checks out!
So my intuition is wrong in thinking that +5% and -4% would become a G.P. of 1%. I feel I am making an important logical error here. Can you guys explain why this line of thinking is incorrect?