Question

5. A credit card company charges its customers a 17.89% APR with continuous compounding. Calculate
the APY using (a) the continuous compounding formula in the textbook, (b) the non-annual compounding
formula in the FE Reference Handbook with m = 1000, and (c) the non-annual compounding formula
in the FE Reference Handbook with m = 10,000.

Answer 1

given i = 17.89 = 0.1789 APR continuous compounding

a)

effective rate = e^i - 1

= e^0.1789 - 1

= 1.1959011 - 1= 0.1959011 = 19.590 %

b) m = 1000

effective rate = (1+ i/m)^m - 1

= (1+ 0.1789/1000)^1000 - 1

= (1.0001789)^1000 - 1

= 1.1958820 - 1 = 0.195882 = 19.588 %

c) m = 10000

effective rate = (1+ i/m)^m - 1

= (1+ 0.1789/10000)^10000 - 1

= (1.00001789)^10000 - 1

= 1.19589923 - 1 = 0.19589923 = 19.589 %