Question

please show work!!

Your bank offers 3-year certificates of deposit with a stated rate of interest of 12% p.a., compounded quarterly. Your cousin (who works at Acme Bank and Trust, a competitor) wants to know what stated rate of interest you would require from them in order to switch your business to their bank. Acme's CD's are compounded on a monthly basis. What is the minimum stated interest rate you should ask for from Acme in order to make you indifferent to switching?

Answer 1

1]

For you to be indifferent, the effective annual rate of both banks should be equal.

Effective annual rate = (1 + (stated rate / n))ⁿ - 1,

where n = number of compounding periods in a year.

Your Bank

Your bank compounds quarterly, hence there are 4 compounding periods in a year.

Effective annual rate = (1 + (stated rate / n))ⁿ - 1

Effective annual rate = (1 + (12%/4))⁴ - 1

Effective annual rate = 12.55%.

Acme Bank

Acme bank compounds monthly, hence there are 12 compounding periods in a year.

The effective annual rate should equal 12.55% for you to be indifferent.

Effective annual rate = (1 + (stated rate / n))ⁿ - 1

12.55% = (1 + (stated interest rate /12))¹² - 1

stated interest rate = ((1 + 12.55%)^1/12 - 1) * 12

stated interest rate = 11.88%.

2]

For you to be indifferent, the effective annual rate of both banks should be equal.

Effective annual rate = (1 + (stated rate / n))ⁿ - 1,

where n = number of compounding periods in a year.

Your Bank

Your bank compounds quarterly, hence there are 4 compounding periods in a year.

Effective annual rate = (1 + (stated rate / n))ⁿ - 1

Effective annual rate = (1 + (10.66%/4))⁴ - 1

Effective annual rate = 11.09%.

Acme Bank

Acme bank compounds monthly, hence there are 12 compounding periods in a year.

The effective annual rate should equal 11.09% for you to be indifferent.

Effective annual rate = (1 + (stated rate / n))ⁿ - 1

11.09% = (1 + (stated interest rate /12))¹² - 1

stated interest rate = ((1 + 11.09%)^1/12 - 1) * 12

stated interest rate = 10.57%.