Final answer:
The effective annual interest rate for semiannual and monthly compounding is 16% and 19% respectively. With semiannual compounding, you earn interest twice a year, while with monthly compounding, you earn interest twelve times a year.
Step-by-step explanation:
The effective annual interest rate for semiannual compounding is 16%. This means that if you invest a certain amount of money that compounds semiannually at a 16% interest rate, you would earn an equivalent annual interest rate of 16%. Let's say you invest $100. After one year, you would earn $16(=$100*0.16). However, with semiannual compounding, you earn interest twice a year. So after the first 6 months, you would earn $8, and after the next 6 months, you would earn $8. The total interest earned for the year would be $16, which is equivalent to the 16% annual interest rate.
For monthly compounding, the effective annual interest rate is 19%. This means that if you invest a certain amount of money that compounds monthly at a 19% interest rate, you would earn an equivalent annual interest rate of 19%. Let's say you invest $100. After one year, you would earn $19(=$100*0.19). However, with monthly compounding, you earn interest twelve times a year. So after the first month, you would earn $1.58, and after the second month, you would earn $1.58, and so on. The total interest earned for the year would be $19, which is equivalent to the 19% annual interest rate.