What is the step by step mathematical formula for the 2 examples below?

1:

Let say we have invested a sum of $1000 with an interest rate of 10% per annum.

If we do not compound, we will just earn $200 bringing you to a total sum of $1200 in a two year period.

However, if we were compounding the interest on the amount annually, we would make more money. In the first year, we would have earned $100 bringing to a total amount of $1100. By compounding interest yearly, the earned $100 will be added to the principal amount and so in the second year, you will earn 10% interest on $1100 which is $110. Making a total sum of $1,210.

2:

Michael saved $1,000 per month from the time he turned 25 until he turned 35. Then he stopped saving but left his money in his investment account where it continued to accrue at a seven percent rate until he retired at age 65.

Jennifer held off and didn't start saving until age 35. She put away $1,000 per month from her 35th birthday until she turned 45. Like Michael, she left the balance in her investment account, where it continued to accrue at a rate of seven percent until age 65.

Sam didn't get around to investing until age 45. Still, he invested $1,000 per month for 10 years, halting his savings at age 55. Then he also left his money to accrue at a seven percent rate until his 65th birthday.

Michael, Jennifer, and Sam each saved the same amount $120,000 over a 10 year period. Let's look at their Returns.