Albert Einstein said that compound interest was "... the most powerful thing I have ever witnessed." Work through the following exercises to discover a pattern Einstein discovered, which is now known as the Rule of 72.
a. Suppose that you invest $2,000 at a 1% annual interest rate. Use your calculator to input different values for t in the compound interest formula. What whole number value of t will yield an amount closest to twice the initial deposit? Express your value in years.

b. Suppose that you invest $4,000 at a 2% annual interest rate. Use your calculator to input different values for t in the compound interest formula. What whole number value of t will yield an amount closest to twice the initial deposit? Express your value in years.

c. Suppose that you invest $20,000 at a 6% annual interest rate. Use your calculator to input different values for t in the compound interest formula. What whole number value of t will yield an amount closest to twice the initial deposit? Express your value in years.

d. Albert Einstein noticed a very interesting pattern when an initial deposit doubles. In each of the three examples above, multiply the value of t that you found times the percentage amount. For example, in part a, multiply t by 1. What number do all instances seem to have in common?

e. Einstein called this the Rule of 72 because for any initial deposit and for any interest percentage, 72 ÷ (percentage) will give you the approximate number of years it will take for the initial deposit to double in value. Einstein also said that "If people really understood the Rule of 72 they would never put their money in banks." Suppose that a 10-year-old has $500 to invest. She puts it in her savings account that has a 1.75% annual interest rate. How old will she be when the money doubles? Express your value in years.