Please show steps for answers so that I can get a better und

(Please show steps for answers, so that I can get a better understanding. Thanks.)

A $100 dollar investment earns 10% the first year, 20% the second year, and 30% the third year. Find a fixed yearly rate which will earn the same amount over the same three years.

Solution

Let the rate of interest be r%

Amount earned in the first year =100*10% =$10

Total amount =110

Amount earned in the second year =110*.2 =$22

Total amount earned =$132

Amount earned in the third year =.3*132 =$39.6

Total interest earned =10+22+39.6 =$71.6

So as a whole the total amount earned =100+71.6 =$171.6

Now ,A=P(1+r/100)^n

Here,A=171.6,n=3 and r=to calculate

171.6=100(1+r/100)^3
Solve for r

we get r=19.7%