Interest Rate

Rates in General §

def. Rate is a simple abstraction of interest rate so that we can calculate things easily.

$$\begin{array}{rlr}R& =\frac{F(\tau )-F(0)}{F(0)}& \text{ (Definition)}\\ & =\tau \cdot r& \text{ (...for simple interest)}\\ & ={\left(1+\frac{r}{k}\right)}^{\tau k}-1& \text{ (...for compound interest)}\end{array}$$

e.g. when banks say they have an APR (Annual Percentage Rate) of 10.99%, their actual rate [=Annual Percentage Yield] is:

$$R={\left(1+\frac{10.99\%}{365}\right)}^{365}-1\approx 11.61\%$$

def. Required Rate of Return (RRR) (=Discount Rate).

• RRR of asset: Minimum amount of profit that the investor will accept
• RRR in general: Average rate of similar-risk investments in the market

def. Internal Rate of Return (IRR).

• Annual rate of growth of an investment.
• Solution of the equation $\text{NPV}(r_{\text{IRR}})\stackrel{\text{set}}{=}0$
  • See NPV calculations

Interest Rate §

Equivalently:

• Discount rate
• Price of Money

Types of interest rates:

1. Yield: interest rate on bonds
2. Mortgage Prime rates
3. LIBOR (inter-bank interest rates)
4. Federal Funds Rate