Answer:
39.34 years
Explanation:
To determine the number of years it will take to double the value of a zero-coupon bond with a stated annual interest rate of 22%, compounded monthly, we can use the formula for compound interest and the concept of the Rule of 72.
The Rule of 72 is a simplified formula that estimates the approximate time it takes for an investment to double based on a given interest rate. According to the Rule of 72, the number of years required to double an investment is approximately equal to 72 divided by the interest rate.
In this case, the interest rate is 22% per year, compounded monthly. To find the monthly interest rate, we divide the annual interest rate by 12:
Monthly interest rate = 22% / 12 = 1.83% (expressed as a decimal)
Using the Rule of 72, we can calculate the number of years required to double the value of the bond:
Number of years = 72 / (monthly interest rate)
Number of years = 72 / 1.83%
Number of years ≈ 39.34 years
Therefore, it will take approximately 39.34 years to double the value of the zero-coupon bond with a stated annual interest rate of 22%, compounded monthly.