# Interest Rate

There are two types of interest rates:

- Simple Interest
- Compound Interest

Compound interest is where it’s at, because it is exponential. Compound Effect.

### Simple Interest

The following single payment equation applies to simple interest: $F=P(1+in)$ where

- $P$ is the principal (present) amount
- $F$ is the future amount
- $i$ is the simple interest rate, and
- $n$ is the period of time

### Compound Interest

The total amount repaid at the end of the $N$ periods is: $F=P(1+i)_{N}$

The total interest on the loan paid at the end of the $N$ periods is: $I_{C}=P(1+i)_{N}−P$

- $I_{C}$ is called compound interest

Compound Interest At Banks

If the interest period and compounding period are not stated, then the interest rate is understood to be annual with annual compounding.

Examples:“12% interest” means that the interest rate is 12% per year, compounded annually.

“12% interest compounded monthly” means that the interest rate is 12% per year (not 12% per month), compounded monthly. Thus, the interest rate is 1% (12% / 12) per month.

### Nominal Interest Rate

The conventional method for stating the annual interest rate (i.e., it is the annual interest rate not including the effect of any compounding during the year). $i_{r}=i_{s}∗m$

Conversely, $i_{s}=mi_{r} $

Ahh so this is kinda useless? Because it doesn’t actually show how the money compounds.

### Effective Interest Rate

The actual interest rate, found by converting a given interest rate with an arbitrary compounding period (less than a year) to an equivalent interest rate with one year compounding period.

$i_{e}=(1+mi_{r} )_{m}−1$

Basically, just look at how much you compound over a given year.

### Continuous Compounding

If only this was possible…