Interest Rates and Fixed Income Instruments

Simple and compound interest

Definition. An amount $A$ invested for n periods at a simple interest rate of $r$per period is worth $A(1+nr)$ at maturity. Definition. An amount $A$ invested for n periods at a compound interest rate of $r$ per period is worth $A(1+r{)}^n$ at maturity. Interest rates are typically quoted on annual basis, even if the compounding period is less than 1 year.

• $n$ compounding periods in each year
• rate of interest $r$
• $A$ invested for $y$ years yields $A(1+\frac{r}{n}{)}^{yn}$ Definition. Continuous compounding corresponds to the situation where the length of the compounding period goes to zero. Therefore, an amount $A$ invested for $y$ years is worth ${\lim }_{x\to \infty }A(1+\frac{r}{n}{)}^{yn}=A{e}^{ry}$ at maturity

Present value

Price p of a contract that pays c = (c_

• c_k > 0
• $c_k>0\equiv$ cash inflow, and $c_k<0\equiv$ cash outflow Present Value (PV assuming interest rate r per period PV(c; r) =