# Financial Mathematics

## Lecture Notes 02

In the second lecture we reviewed the definitions of interest and interest rate. We learned the simple interest formula and we looked at the methods for calculating credit card interest from another angle.
The terms we defined in the lecture are:

1. interest (Interest is the fee paid by the borrower to the owner. It is denoted by I.)
2. interest rate(Interest rate is the percentage of the amount borrowed charged to the borrower for a fixed amount of time. It is denoted by i.)
3. principal(Principal is the amount of money borrowed. It is denoted by P.)
4. term(The term is the length of the loan in time units. It is denoted by t.)
5. maturity value (The maturity value is the amount of money the borrower will pay back.

The simple interest formula is:
$I = Pit$

This means the interest is the principal times the interest rate times the term. Be careful to express the fixed time interval in the interest rate in the same units of measurement.
The maturity value is denoted by S. The formula is:

$S = P + I = P + Pit = P\left(1+it\right)$

I will provide a few more details for the last example from class:
Guido the Enforcer offers you a simple interest loan of \$1,000 at 3% weekly rate. Is this a good deal or a bad one?
Lets look at the interest paid for a loan with the term one week. In this case

$I = Pit = 1,000 x 0.03/week x 1 week = 30$

This may not seem to be a bad deal. After all \$30 compared to \$1,000 is not that much.
Let’s calculate the equivalent interest rate per year (see class slides).

$i = 3%/week = 3%/\left(1/52\right)year = 156%/year$

This is pretty steep.