This question from Hull's Options Futures and Other Derivatives text is really messing with my head. It's Example 4.2 on Pg. 78 of the 7th Edition. Goes like this:
"Suppose that a lender quotes the interest rate on loans as 8% per annum with continuous compounding, and that interest is actually paid quarterly...the equivalent rate with quarterly compounding is 4 x [e^(0.08/4) - 1] = 0.0808, or 8.08% per annum. This means that on a $1,000 loan, interest payments of $20.20 would be required each quarter."
This doesn't make any sense?? How can the interest be the same each quarter? If they have a quarterly compounding rate, then doesn't the rate apply to the new sum each quarter (ie principal + newly earned interest). As well, with continuous compounding, you should end up with $1,083.29 at the end of the year, but in their example with equal quarterly interest payments, you would only get $1,080.80 at the end of the year. Am I missing something here?
"Suppose that a lender quotes the interest rate on loans as 8% per annum with continuous compounding, and that interest is actually paid quarterly...the equivalent rate with quarterly compounding is 4 x [e^(0.08/4) - 1] = 0.0808, or 8.08% per annum. This means that on a $1,000 loan, interest payments of $20.20 would be required each quarter."
This doesn't make any sense?? How can the interest be the same each quarter? If they have a quarterly compounding rate, then doesn't the rate apply to the new sum each quarter (ie principal + newly earned interest). As well, with continuous compounding, you should end up with $1,083.29 at the end of the year, but in their example with equal quarterly interest payments, you would only get $1,080.80 at the end of the year. Am I missing something here?