Yousaf K.

asked • 12/06/13

comparing the interest rates

John needs to borrow $500,000 for three years. Which of the following option is more beneficial for him?
(i) 3.2 % simple interest rate
(ii) 1.6% compound interest rate when it is compounded semi annually

2 Answers By Expert Tutors

By:

Maurizio T. answered • 12/06/13

Tutor
5.0 (923)

Statistics PhD and CFA charterholder with a true passion for teaching.

Kenneth G.

I looked up the term "compound interest rate" online, and the response is:
"Phrase not found in the Dictionary and Encyclopedia. Please try the words separately"

In my view, it's not reasonable to interpret the problem this way.
Report

12/06/13

Kenneth G. answered • 12/06/13

Tutor
New to Wyzant

Experienced Tutor of Mathematics and Statistics

Maurizio T.

Kenneth, it is quite possible that they meant that and that is the standard approach. But the 1.6% is not qualified as an "annual nominal interest rate". The lack of "annual" leaves the door open to interpretations. Of course, comparing an annual interest rate of 1.6% vs. one of 3.2% (albeit simply compounded) does not even require calculations to tell which one is the best option of the two for this lucky John. Even if one compounded the 1.6% continuously, you would only pay $500,000*e.016*3 = $524,585.33. 
Report

12/07/13

Maurizio T.

i.e. only $24,585.33 of interest vs. a whooping $48,000 choosing the first option.
 
Report

12/07/13

Kenneth G.

Maurizio,
I agree with you. It's not a bad thing that you posted a different interpretation of the problem. It illustrates that there can be alternate interpretations of a mathematical problem. Students need to understand that there is not necessarily one right answer in Mathematics, and that there can be different interpretations of a math problem.

By stating that my interpretation was incorrect (which it might have been if the problem had been worded better) you didn't allow for my interpretation and didn't check to make sure the term “compound interest rate” was well defined, which is why I posted my comment to your solution.
 
Report

12/07/13

Maurizio T.

Kenneth,
I do not believe I wrote that your interpretation is incorrect. In fact, I even wrote that "it is quite possible that they meant that"; i.e., what you wrote, and added that, in general, it would be the standard approach as a matter of fact. I just pointed out that the 1.6% lacks the qualification of "annual" which is usually required. I apologize if I gave you that impression.
 
Ultimately, there is no doubt that the wording of the problem is ambiguous and open to interpretations. As a student, I would have clarified with my teacher/professor/instructor what is the meaning of that 1.6%.
Report

12/07/13

Kenneth G.

I agree.  Thanks for the great discussion!
Report

12/08/13

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.