Final answer:
An investment at a 14% interest rate compounded quarterly will take approximately 5.26 years to double in value using the compound interest formula.
Step-by-step explanation:
To calculate how long it takes for an investment to double in value at an interest rate of 14% compounded quarterly, we can use the Rule of 72 or the compound interest formula. The Rule of 72 is a simple way to estimate the number of years required to double the investment by dividing 72 by the annual interest rate. However, since the interest is compounded quarterly, we need to adjust the rate and the time.
For a more precise calculation, the compound interest formula 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.
To find the time (t) when the investment doubles, A is 2P. Thus, the equation becomes 2P = P(1 + 0.14/4)(4t). Solving for 't' gives us the time needed for the investment to double. For an interest rate of 14% compounded quarterly, this calculation gives us approximately 5.26 years.