Question

An account will pay 4.64% APR with quarterly compounding, but payments will only be made from the account twice per year. (every two quarters). What is the proper rate to apply to the semi-annual payments on the account?

Answer 1

Annual Interest Rate = 4.64% compounded quarterly

Quarterly Interest Rate = 4.64% / 4
Quarterly Interest Rate = 1.16%

Effective Annual Rate = (1 + Quarterly Interest Rate)^4 - 1
Effective Annual Rate = (1 + 0.0116)^4 - 1
Effective Annual Rate = 1.0472 - 1
Effective Annual Rate = 0.0472 or 4.72%

Semiannual Interest Rate = (1 + Effective Annual Rate)^(1/2) - 1
Semiannual Interest Rate = (1 + 0.0472)^(1/2) - 1
Semiannual Interest Rate = 1.0233 - 1
Semiannual Interest Rate = 0.0233 or 2.33%

Annual Interest Rate = 2 * Semiannual Interest Rate
Annual Interest Rate = 2 * 2.33%
Annual Interest Rate = 4.66% compounded semiannual