1 If the nominal interest rate is 18 what is the effective a

1. If the nominal interest rate is 18%, what is the effective annual interest rate when interest is compounded: a) Annually b) Semiannually c) Quarterly d) Monthly e) Daily 2. If the effective annual rate is 6.14% and compounding occurs monthly, what is the nominal rate? 3. If the effective annual rate is 12%, what is the nominal interest rate when interest is compounded: a) Annually b) Semiannually c) Quarterly d) Monthly e) Daily

Solution

1. Nominal Interest Rate (NIR) = 18% = 0.18

Effective Annual Interest Rate (EAIR) = NIR / Number of Compounding Periods within the year.

(a) EAIR when compounded Annually = 0.18 / 1 = 0.18

(b) EAIR when compounded Semi-Annual = 0.18 / 2 = 0.09

(c) EAIR when compounded Quarterly = 0.18 / 4 = 0.045

(d) EAIR when compounded Monthly = 0.18 / 12 = 0.015

(e) EAIR when compounded Daily = 0.18 / 365 = 0.000493