Question

(a) What interest rate compounded monthly is equivalent to (has the same APY as) 15% compounded semi-annually? (b) What interest rate compounded continuously is equivalent to (has the same APY as) 15% compounded semi-annually?

Answer 1

(a) What interest rate compounded monthly is equivalent to (has the same APY as) 15% compounded semi-annually?

Effective Annual rate = ( 1 + Interest per period)^Periods per year] - 1

Effective Annual rate = 1.075^2 - 1

Effective Annual rate = 15.56%

Nominal Interest Rate Compounded monthly = (1 + Effective Interest Rate)^(1/Periods per year) - 1] * Periods per year

Nominal Interest Rate Compounded monthly = 1.1556^(1/12)-1] * 12

Nominal Interest Rate Compounded monthly = 1.01213-1] * 12

Nominal Interest Rate Compounded monthly = 14.55%

(b) What interest rate compounded continuously is equivalent to (has the same APY as) 15% compounded semi-annually?

Effective Annual rate = ( 1 + Interest per period)^Periods per year] - 1

Effective Annual rate = 1.075^2 - 1

Effective Annual rate = 15.56%

Nominal Interest Rate Compounded Continuously = Ln(1 + Effective Interest rate)

Nominal Interest Rate Compounded Continuously = Ln(1.1556)

Nominal Interest Rate Compounded Continuously = 14.46%