Question 1: Compound Interest

It is a US Treasury market's convention to use semi-annual compounding rate in quoting bond yields and in calculating bonds' price. However, some corporate and sovereign bonds pay coupons at an annual frequency. So it is useful to review the impact of different compounding periods. In general, given the quoted APR r, you may want to compound m times per year for N years.

Write down the formula for the value of an initial investment, $A, compounding weekly at rate r for 10 years. How many years (T) does it take to double your money under different assumptions for the compounding frequency (m) and interest rate (r)? Fill out the table below using daily, weekly, monthly, and semi-annual compounding; and annual interest rates of 1%, 2%, and 12% percent. Write down the general formula for the answer. What APR, when compounded semi-annually, yields the same amount of money after one year as a 5% annual rate (compounded annually) yields after one year?