Question

Please describe the effective rate of return? What are the effective rates of return on a 5% annual rate of return if compounded daily, weekly, monthly and, annually. Would you prefer more frequent compounding or less if you are lending money and why?

Answer 1

Please describe the effective rate of return?

Effective rate of return (ERR) is the actual rate of an investment. This is a a measure of actual rate returned by the investment and not the nominal rate.

The formula for Effective rate of return is:

where r = nominal interest rate on the investment and n = number of periods in a year.

What are the effective rates of return on a 5% annual rate of return if compounded daily, weekly, monthly and, annually.

If compounded daily, n = 365, Hence ERR = (1 + 5% / 365)³⁶⁵ - 1 = 5.1267%

If compounded weekly, n = 52 (assuming 52 weeks in a year), Hence ERR = (1 + 5% / 52)⁵² - 1 = 5.1246%

If compounded monthly, n = 12, Hence ERR = (1 + 5% / 12)¹² - 1 = 5.1162%

If compounded annually, n = 1, Hence ERR = (1 + 5% / 1)¹ - 1 = 5.0000%

Would you prefer more frequent compounding or less if you are lending money and why?

We can see above that higher frequency of compounding results into a higher effective rate of return. This in turn will lead to a higher future value of the investment. Hence, if I am a lender, I will prefer more frequent compounding.