A principal earns 7.5% per year simple interest. How long will it take for the future value to quadruple?
1.075^x = 4
oops. That was compound.
.075x = 3
To find out how long it will take for the future value to quadruple, we need to use the formula for simple interest:
Simple Interest = Principal * Interest Rate * Time
Let's assign some variables to the given values in the problem:
Principal = P
Interest Rate = 7.5% = 0.075 (decimal)
Time = T (unknown)
We know that the future value should be four times the original principal amount:
Future Value = 4 * Principal = 4P
Substituting these values into the formula, we get:
Simple Interest = P * 0.075 * T
Since the future value should be quadruple the original principal (4P), we can set up the equation:
4P = P * 0.075 * T
We can simplify the equation by canceling out the common factor of P:
4 = 0.075 * T
Now, divide both sides of the equation by 0.075 to isolate the variable T:
T = 4 / 0.075
Evaluating this expression, we find:
T ≈ 53.33
Therefore, it will take approximately 53.33 years for the future value to quadruple at a 7.5% simple interest rate.