Question

An interest rate is 7% per annum with continuous compounding. What is the equivalent rate with quarterly compounding? Choose from the following;

6.96%

7.06%

6.26%

7.16%

Answer 1

Answer is 7.06%

Annual Interest Rate = 7.00% compounded continuously

Effective Annual Rate = exp(Annual Interest Rate) - 1
Effective Annual Rate = exp(0.07) - 1
Effective Annual Rate = 1.07251 - 1
Effective Annual Rate = 0.07251 or 7.251%

Quarterly Interest Rate = (1 + Effective Annual Rate)^(1/4) - 1
Quarterly Interest Rate = (1 + 0.07251)^(1/4) - 1
Quarterly Interest Rate = 1.01765 - 1
Quarterly Interest Rate = 0.01765 or 1.765%

Equivalent Annual Rate = 4 * Quarterly Interest Rate
Equivalent Annual Rate = 4 * 1.765%
Equivalent Annual Rate = 7.06% compounded quarterly