Final answer:
To find the time to double an investment at a 14% annual rate compounded monthly, use the compound interest formula. With a 14% annual rate compounded monthly, divide the rate by 12, and solve the compound interest formula for the time.
Step-by-step explanation:
To calculate how long it takes for an investment to double in value when it's compounded monthly at a 14% annual interest rate, we can use the Rule of 72. This is a simple way to estimate the number of years required to double the invested money at a given annual fixed interest rate. By dividing 72 by the annual interest rate, you can get a rough estimate. However, because we are dealing with monthly compounding, the formula needs to be adjusted slightly.
The compound interest formula to use in this case is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time in years.
We want the final amount A to be double the principal P. Therefore, the formula becomes 2P = P(1 + r/n)^(nt). With a 14% annual rate compounded monthly, r is 0.14, and n is 12. After simplifying the equation, we can solve for t, which represents the time in years needed for the investment to double.