Assume that bank A offers 5 percent compounding monthly, while bank B offers 5.1 percent compounding quarterly. Which bank should we borrow from in order to enjoy a lower interest rate? These examples are associated with conversion between different interest rates. First, let's look at the following formula used to estimate effective annual rate (EAR) for a given Annual Percentage Rate (APR).

Here, m is the compounding frequency within one year. For example, if the annual rate is 5 percent compounding semiannually, its equivalent effective annual rate will be 5.0625 percent. From the two banks' offers, we would choose the offer of bank A since the cost of borrowing (effective annual rate) is cheaper, as shown in the following code:

>>>(1+0.05/2)**2-1
0.05062499999999992
>>>(1+0.051/4)**4-1
0.051983692114066615

For a mortgage estimate, if the annual rate is 5 percent, compounding monthly, the effective monthly rate will be 0.41667 (0.05/12)....