Question

Find the EAR in each of the following cases: SHOW WORK

Stated Rate (APR) Number of Times Compounded Effective Rate (EAR)

9% Quarterly ?

18% Monthly ?

14% Daily ?

11% Infinite ?

Answer 1

r = (1+i/n)^n - 1

where e - effective interest rate

n - no. of compounding periods

r = (1+.09/4)^4 - 1

= (1+0.0225)^4 - 1

= 1.0225^4 - 1

= 1.093083 - 1

= 0.093083

= 9.31%

2nd case - where APR = 18% compounded monthly

r = (1+.18/12)^12 - 1

= (1+0.015)^12 - 1

= 1.015^12 - 1

= 1.195618 - 1

= 0.195618

= 19.56%

3rd case where APR = 14% compounded daily

r = (1+.14/365)^365 - 1

= (1+0.000383562)^365 - 1

= 1.000383562^365 - 1

= 1.15024 - 1

= 0.15024

= 15.02%

4th case- APR = 11% continuous compounded

A = e^(i/k) - 1

where I - interest rate

k = 1

where value of e constant = 2.71828^.11 -1

= 1.116278 - 1

= .116278

11.62%

Please check with your answer an let me know.