A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3% per year, you will need to make $33,598 in 10 years to have the same buying power. You will need to make $44,771 in the inflation rate jumped to 6%. Confirm the statements are accurate by finding the geometric mean rate of increase.

Not sure where to put the numbers in the formula and want to confirm the formula. Since it is between two periods -

GM=n/sqroot value at the end of the period divided by value at the beg of the period.

25,000 x 1.03^10 = 33,598
25,000 x 1.06^10 = 44,771

Therefore, the statements are correct.

GM=n/sqroot value at the end of the period divided by value at the beg of the period.

Where did you get your formula from? It's not correct.

Given:

V_i= initial\ value


V_f= final\ value


N= number\ of\ years


the formula for calculating the geometric mean (also known as the exponential growth rate) is:

R = \left( \frac {V_f} {V_i} \right)^{\frac 1 N}


Using your first example you find that R = (33598/25000)^1/10 = 1.03, which confirms that it corresponds to a 3% growth rate per year.