In: Finance
(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?
(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%