# Financial Mathematics

## Lecture Notes 03

In lecture 3 we learned about exact and approximate time and ordinary and exact interest.

I will discuss a little bit the last clicker question:
Which interest type is better for the borrower?
A) Ordinary interest (divide by 360)
B) Exact interest (divide by 365)
C) They are the same
D) Depends on the term of the loan

The correct answer is B or D, depending on what you think “better” means. More precisely, if “better” means smaller or equal then the correct answer is B; if “better” means strictly smaller, then the correct answer is D.

In the analysis below we assume we use exact time.

If Alice takes out a loan on 5 September 2011 with maturity date 5 September 2012, the the term is exactly 1 year. In this case, both ordinary interest and approximate interest are calculated using the formula I = P i 1 year. Thus the two methods give the same answer.

The two types of interest will give you a different answer when the term contains a fraction of a year. Assume the term is one day. The ordinary interest formula is I = P i 1/360. The exact interest formula is I = P i 1/365. In this case, the exact interest is better for the borrower. As Matt pointed today, whenever you divide by a bigger number the result is smaller.

The point I was trying to make is you have to divide by 360 or 365 only when your term is a whole number of years plus some days.