Effective Annual Rate (EAR)

First National Bank charges 10.1 percent compounded monthly on its business loans. First United Bank charges 10.4 percent compounded semiannually. As a potential borrower, to which bank would you go for a new loan?

First National Bank, r = 10,1 percent , m = 12

First United Bank, r = 10,4 percent, m = 2

( 1+ 0,101/12)¹² = 1,1007  , EAR = 1,10079 – 1 = 0,10079 = 10,08 %

 (1+0,104 / 2)² = $ 1,106 EAR = 1,1067 – 1 = 0,1067 = 10,7 %

As a potential borrower, I would go for First National Bank, which charges 10,08 %. Rather than go to First United bank which charges 10,6 %.

illustration image: bridge inside campus, would go for first national bank

Explanation about EAR (Effective Annual Rate):

More generally, compounding an investment m times a year provides end- of- year wealth of:

C₀ (1 + r / m )^m

Effective Annual Rate:

(1 + r / m) ^m – 1

Example – Compounding Frequencies

If the stated annual rate of interest, 8 percent, is compounded quarterly, what is the effective annual rate?

EAR = (1+ r/m)^m – 1

(1+ 0.08/4)⁴ – 1

=0.0824

=8,24%

Note:

Yearly (m = 1)

Semiannually (m= 2)

Quarterly ( m = 4)

Monthly ( m = 12)

Daily (m=365)

APR (Annual Percentage Rate) = EAR (Effective Annual Rate) if m = 1

reference: Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.