A bank offers the following choices for certificates of deposit: Year one: 4% no

Question

A bank offers the following choices for certificates of deposit:

Year one: 4% nominal interest rate convertible quarterly

Year three:5% nominal interest rate convertible quarterly

Year 5: 5.65% nominal interest rate convertible quarterly

Ther certificates mature at the end of the term. the bank does not permit early withdrawals. during the next 6 years the bank will coninue to offer certificates of deposit with the same terms and interest rates. an investor initially deposits 10,000 in the bank and withdraws both principal and interest at the end of 6 years. calculate the max annual effective rate of interest the investor can earn over the 6 year period.

A. 5.09%, B. 5.22%, C. 5.35%, D. 5.48%, E. 5.61%

Explanation / Answer

There are only two real possibilities:

Two consecutive 3 year CDs:

=10000 * (1+(0.05/4))^12 * (1+.(0.05/4))^12 = 13, 473.51

One 5 year CD and a 1 year CD:

=10000 * (1+(0.0565/4))^20 * (1+.(0.04/4))^4 = 13,775.75

13,775.75 is the greater.

The annual effective rate is

=10000 * (1+I)^6 = 13,775.75

i = 5.48%

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