The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

43. Find the effective rate equivalent to 6.45% compounded annually.

H. Additional Exercises

44. Tamara walked into the lobby of her bank and saw the following sign:

New Account Spectacular!

Open a new 6-month CD and enjoy a 5.25% interest rate!

(Effective rate 5.18%)

She immediately knew that whoever wrote the sign had made a mistake. How did she know?

45. Marta opened a CD for 2 years that paid an effective rate of 8%. At the end of its term, she took the proceeds and
    invested them in a new 2-year CD that paid a 12% effective rate. At the same time as Marta opened her original
    account, Dylan opened up a 4-year CD paying an effective rate of 10%. Both Marta and Dylan started by depositing
    the same amount of money. Who had more at the end of 4 years?


46. Portageville Savings and Loan offers a 3.25% nominal rate on its savings accounts, compounded monthly. What interest
    rate compounded quarterly would be equivalent to this rate?


47. Find the effective rate equivalent to 6% compounded continuously.


48. The population of Waldburg is presently 58,273 and is predicted to decline at a 1.4% annual rate in the future.
    According to this prediction, what will the population be in 20 years?

3.4 Comparing Effective and Nominal Rates 127

3.4 Comparing Effective and Nominal Rates

In the previous section we developed the idea of an annually compounded rate equivalent

to a given nominal rate. In this section, we will explore this equivalence, and take note of

some issues in using effective rates in place of nominal ones.

If we know the effective rate for a given nominal rate, it would seem that we could use

the two rates interchangeably. This is true, by and large, as the following examples will

illustrate.

Example 3.4.1 Melvin deposited $1,896 in a savings account for 4 years at

3.98% compounded daily. In the previous chapter, we found that this nominal rate is

equivalent to 4.06% compounded annually. Find his future value using both rates and

compare the results.

Nominal rate: FV
$1,896  1  0.0398___ 365 

1,460


 $2,223.18

Effective rate: FV 
 $1,896(1.0406)^4 
 $2,223.17

The answers are not exactly the same, but they are very close.

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