Final answer:
The interest rates with different compounding periods are: (a) 10.3025%, (b) 10.3908%, (c) 10.5826%, (d) 10.6647%, and (e) 10.7407%.
Step-by-step explanation:
(a) Semiannual compounding:
The interest rate can be expressed as:
Effective Annual Rate (EAR) = (1 + periodic interest rate)number of periods - 1
For semiannual compounding, the periodic interest rate is half the annual rate:
Periodic interest rate = 11% / 2 = 5.5%
Substituting the values into the formula:
EAR = (1 + 5.5%)2 - 1
Calculating the EAR:
EAR = 11.3025% - 1 = 10.3025%
(b) Quarterly compounding:
For quarterly compounding, the periodic interest rate is a quarter of the annual rate:
Periodic interest rate = 11% / 4 = 2.75%
Substituting the values into the formula:
EAR = (1 + 2.75%)4 - 1
Calculating the EAR:
EAR = 11.3908% - 1 = 10.3908%
(c) Monthly compounding:
For monthly compounding, the periodic interest rate is a twelfth of the annual rate:
Periodic interest rate = 11% / 12 = 0.9167%
Substituting the values into the formula:
EAR = (1 + 0.9167%)12 - 1
Calculating the EAR:
EAR = 11.5826% - 1 = 10.5826%
(d) Weekly compounding:
For weekly compounding, the periodic interest rate is 1/52 of the annual rate:
Periodic interest rate = 11% / 52 = 0.2115%
Substituting the values into the formula:
EAR = (1 + 0.2115%)52 - 1
Calculating the EAR:
EAR = 11.6647% - 1 = 10.6647%
(e) Daily compounding:
For daily compounding, the periodic interest rate is 1/365 of the annual rate:
Periodic interest rate = 11% / 365 = 0.0301%
Substituting the values into the formula:
EAR = (1 + 0.0301%)365 - 1
Calculating the EAR:
EAR = 11.7407% - 1 = 10.7407%