Find the EAR in each of the following cases: a. 19% compounded quarterly.
b. 15% compounded monthly.
c. 19% compounded daily.
d. 16% with continuous compounding.

a. 20.40 %

b. 16.08 %

c. 20.92 %

d. 17.35 %

Explanation:

Effective Annual Interest Rate is the annual rate that if compounded once a year, would give us the same result as the interest per period compounded a number of times per year.

Effective Annual Interest Rate = ( 1 + i/m)^m -1

a. 19% compounded quarterly.

Effective Annual Interest Rate = ( 1 + 0.19/4)^4 -1

                                                  =  20.40 %

b. 15% compounded monthly.

Effective Annual Interest Rate = ( 1 + 0.15/12)^12 -1

                                                  = 16.08 %

c. 19% compounded daily.

Effective Annual Interest Rate = ( 1 + 0.19/365)^365 -1

                                                  = 20.92 %

d. 16% with continuous compounding.

Effective Annual Interest Rate = e^i - 1

                                                  = e^(0.16) -1

                                                  = 17.35 %

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