in 2000, Sam opened an account paying 5.2% annual interest. Has his money doubled yet? if so, when did it. If not when will it? I believe this is simple interest, for it is not stated.
years to double is ... 100% / 5.2%
To determine whether Sam's money has doubled or not, let's first calculate how many years it would take for an initial amount to double at an annual interest rate of 5.2%.
The formula we can use to calculate the future value of an investment with simple interest is:
Future Value = Principal + (Principal x Interest Rate x Time)
In this case, we want to find out when the Future Value is double the Principal. Therefore, we can rewrite the formula as:
2 * Principal = Principal + (Principal x Interest Rate x Time)
To simplify further, we can cancel out the Principal on both sides:
2 = 1 + (Interest Rate x Time)
Next, subtract 1 from both sides:
1 = Interest Rate x Time
Finally, divide both sides by the Interest Rate:
Time = 1 / Interest Rate
Substituting in the given annual interest rate of 5.2% (or 0.052 as a decimal):
Time = 1 / 0.052
Time ≈ 19.2308 years
So, it would take approximately 19.2308 years for Sam's money to double at an annual interest rate of 5.2%.
Now, to determine whether the money has already doubled or not, we need to find the difference between the current year (2021) and the year when Sam opened the account (2000).
2021 - 2000 = 21 years
Since 21 years have passed since Sam opened the account, and the money would double in approximately 19.2308 years, we can conclude that Sam's money has already doubled.
Therefore, Sam's money doubled sometime between the years 2000 and 2021.