## Instantaneous spot interest rate

Interest Rates Definition 1.1 (Zero-coupon bond). The continuously-compounded spot interest rate with maturity T prevail- is the instantaneous rate at which the bank accrues, where the bank account is deﬁned as B(t)=exp t 0 r(s)ds. The short rate is also used to deﬁne the discount factor Instantaneous and Compounded Annual Rates for Interest In finance there are two ways to express rates such as interest rates. The most common way is as the effective annual rates so that if the interest rate is r then $1 deposited at the beginning of a year will grow to be (1+r) by the end of the year.