Question

A bank offers the following certificates of deposit: Nominal annual interest rate Term in years (convertible quarterly) 1 4% 3 5% 5 5.65% The bank does not permit early withdrawal. The certificates mature at the end of the term. During the next six years the bank will continue to offer these 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 six years. Calculate the maximum annual effective rate of interest the investor can earn over the 6-year period.

Answer 1

Answer:

i = 5.48%

Explanation:

We can use the following method to solve the given problem in the question.

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%

Answer 2

Answer:

5.48%

Explanation:

Effective interest rate is the actual interest rate that a investor receives on investment or a borrower pays on loan including the compounding effect.

Here we have two possibilities

Two consecutive 3 year CDs:

Future value  = 10,000 x ( 1 + ( 5%/4 ) )^12 x ( 1 + ( 5%/4 ) )^12 = $13, 473.51

One 5 year CD and a 1 year CD:

Future value  = 10,000 x ( 1 + ( 5.65%/4 ) )^20 x ( 1 + ( 4%/4 ) )^4 = $13,775.75

As $13,775.75 is the greater the investor will prefer this combination.

Now calculate the Effective interest rate

$10,000 x ( 1 + i )^6 = 13,775.75

i = 5.48%