Doubts

Exercise 2 from Lecture 2 (in class)

Exercise 2 from Lecture 2 (in class)

by Xenia Lorej -
Number of replies: 3

Dear Julio,

I have a question about exercise 2 from lecture 2. Why do we continue to calculate with the APR instead of converting it to the EAR first?

We first initially converted the 5% to 5.1% using the EAR formula and then we arrived at a monthly rate of 0.00415%.

In Review Quiz 2, a similar exercise also uses the EAR for the annuity formula, just as in the lecture explained. 


Thank you very much for your time and guidance.

In reply to Xenia Lorej

Re: Exercise 2 from Lecture 2 (in class)

by Julio Crego -
Dear Xenia,

I do not know which Review quiz exercise you are referring to. You can compute the EAR if you prefer

- EAR: \(1.025^2=5.0625\)
- Effective monthly rate is \(5.0625^{\frac{1}{12}}\)

The result is the same. We need to use monthly rates because they are monthly payments. 
In reply to Julio Crego

Re: Exercise 2 from Lecture 2 (in class)

by Alois Jari Thomas Neff -
Dear Julio,

Just to make sure. So in the case of monthly payments, we always have to calculate the monthly rate, even though the compounding is only semi-annual? So we can't take the monthly payment times six and use the semi-annual effective rate instead because of the time value of money, or why?

Thank you very much in advance!
In reply to Alois Jari Thomas Neff

Re: Exercise 2 from Lecture 2 (in class)

by Julio Crego -
Yes, always.

Good question. There is a difference between compounding frequency and the payment frequency. Intuitively, compounding frequency reflects how often you reinvest the proceeds of an alternative investment. Yet, when we receive a payment in 3 months, we like it better than receiving it in 5 months (even if we compound semi-annually). Therefore, discounting always happens considering the time to get the payment.