Final answer:
To determine how long it takes for an investment to double in value with a 16% compound interest rate compounded monthly, we can use the formula for compound interest and solve for the number of years. In this case, it would take approximately 4.81 years.
Step-by-step explanation:
To determine how long it takes for an investment to double in value with a 16% compound interest rate compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the ending value, P is the principal (initial investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we want to find the value of t when the ending value (A) is double the principal (2P). Plugging in the values into the formula:
2P = P(1 + 0.16/12)^(12t)
Dividing both sides by P and simplifying:
2 = (1 + 0.16/12)^(12t)
Taking the natural logarithm of both sides and using log properties:
t = ln(2) / (12 * ln(1 + 0.16/12))
Calculating the value:
t = 4.81 years