nominal rates do not reflect the actual cost of

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Unformatted text preview: d) Never, ever, EVER, use a nominal interest rate to discount or compound cash flows!!! - Never use ‘(1+im)’ for anything and never ­ever put ‘im’ into a denominator! - Nominal rates do not reflect the actual cost of lending/borrowing. - The only thing a nominal rate is good for is to compute the corresponding effective periodic rate. - This effective rate can then be used to compute effective rates for different compounding frequencies. What is the nominal interest rate isemi that yields the same return as a monthly interest rate rmo of 1%? – a) 6.00% – b) 12.00% – c) 12.30% – d) 6.15% – e) None of the above – Correct answer is c) Why Stop Here? Taking Compounding to the Limit - We don t have to stop at monthly or daily compounding. Interest rates could be compounded every hour, every second, or every infinitesimally small time interval. - We call this limit ‘continuous compounding.’ - So what happens if interest is compounded continuously (or instantaneously) ? Will the EAR explode or will there be an upper limit? - One can show that: – where e is the base of the natural log (e = 2.718281828.....) The natural log is denoted by ‘ln’. Recall that with daily compounding, the effective annual rate that yielded the same return as 12% compounded daily is equal to 12.7475% - So the difference between daily compounding and continuous compounding is relatively small....
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