Question

Which of the following accounts has the highest EAR?

	a.	one that pays 6% every six months.
	b.	one that pays 12% annually.
	c.	one that pays 1% every month.
	d.	one that pays 3% quarterly.

Answer 1

The account, which pays 1% every month has the highest EAR.

APR is same for all the four accounts. So, the account with highest compounding frequency has highest EAR. Let’s compute effective rate for each account to compare.

Effective rate = (1+ r/m) ^m – 1

r = Stated rate or APR

m = Annual compounding frequency

a.

r/m = 0.06; m = 2

Effective rate = (1+ 0.06) ² – 1

                        = (1.06) ² – 1

                        = 1.1236 – 1

                        = 0.1236 or 12.36 %

b.

r/m = 0.12; m = 1

Effective rate = (1+ 0.12) ¹ – 1

                        = 1.12– 1

                        = 0.12 or 12 %

c.

r/m = 0.01; m = 12

Effective rate = (1+ 0.01) ¹² – 1

                        = (1.01) ¹² – 1

                        = 1.12682503013197 – 1

                        = 0.12682503013197 or 12.68 %

d.

r/m = 0.03; m = 4

Effective rate = (1+ 0.03) ⁴ – 1

                        = (1.03) ⁴ – 1

                        = 1.12550881 – 1

                        = 0.12550881 or 12.55 %

Monthly compounding account has highest EAR.

Hence option “c. one that pays 1% every month” is correct answer.