Wee Willy comes from humble beginnings or so he thought His

Wee Willy comes from humble beginnings, or so he thought. His parents were hard working people, but they never seemed to have 2 pennies to rub together. When Mr. and Mrs. Willy retired in 1941, they earned a small pension and had $5,000 in a savings account. At the time of their death, simultaneously in an air crash in 19.95, they were both 98 years old. Their will concluded Mr. and Mrs. Willy had turned their $5,000 into $22 million through some shrewd investing, and they were leaving all of it to Wee Willy. What annual rate of return compounded annually would turn $5,000 into $22 million for that amount of time?

Solution

Formula for annual compounding:

Amount = Principal( 1 +r)^t

where r is interest rate and t is time

22000,000 = 5000( 1 +r)^98

4400 = (1 +r)^98

taking log on both sides:

ln(4400) = 98ln(1+r)

0.085 = ln(1 +r)

1.0887 = 1 +r

r = 0.0887 = 8.87% annual rate of interest