Question

Find the EAR in each of the following cases. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. Use 365 days in a year.)

HW: Chapter 5 (5.3 & 5.4) i Saved Find the EAR in each of the following cases. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. Use 365 days in a year.) Effective Rate (EAR) points Stated Rate (APR) ato (ADD 9.75 % 16.25 % 15.75 % 11.75 % Number of Times Compounded Quarterly Monthly Daily Semiannually eBook

Answer 1

The formula for Effective annual interest rate (EAR) is
EAR = (1+i/n)^n - 1
where i is the stated rate
and n is the number of compounding periods
1)
i = 9.75%
n = 4
EAR = (1+.0975/4)^4 - 1
EAR = (1+.024375)^4 - 1
EAR = (1.024375)^4 - 1
EAR = 1.101123 - 1
EAR = .101123
The EAR is 10.11%.
2)
i = 16.25%
n = 12
EAR = (1+.1625/12)^12 - 1
EAR = (1.013542)^12 - 1
EAR = (1.175166 - 1)
EAR = .175166
The EAR is 17.52%.
3)
i = 15.75%
n = 365
EAR = (1+.1575/365)^365 - 1
EAR = (1+.000432)^365 - 1
EAR = (1.000432)^365 - 1
EAR = 1.170541 - 1
EAR = .170541
The EAR is 17.05%.
4)
i = 11.75%
n = 2
EAR = (1+.1175/2)^2 - 1
EAR = (1.05875)^2 - 1
EAR = 1.120952 - 1
EAR = .120952.
The EAR is 12.09%.

Answer 2

SOLUTION :

Stated rate                 Number of times                   Effective rate

  (APR)                          compounded                            (EAR)

  9.75%                              Quarterly                  (1 + 0.0975/4)^4 - 1 = 0.1011 = 10.11%

 16.25%                             Monthly                 (1 + 0.1625/12)^12 - 1 = 0.1752 = 17.52%

 15.75%                             Daily                  (1 + 0.1575/365)^365 - 1 = 0.1705 = 17.05%

 11.75%                     semiannually                     (1 + 0.1175/2)^2 - 1 = 0.1210 = 12.10%