Pt is the current market price of T-year interest-free bonds, Mt is the maturity value, and st is the T-year spot interest rate.

For example, the annual ticket =1000 *10% =100 yuan.

Assuming that the three-year spot interest rate is t, there are:100/(1+5%)+100/(1+6%) 2+1100/(/. t=4.87%

The forward interest rate from the second year to the third year is set as I: (1+t) 3 = (1+6%) 2 * (1+i); Solution, i=2.65%.

Extended data:

Considering the change of interest rate with the length of the term, people have adopted such a method, that is, discounting cash flows with different terms with different interest rates. This interest rate that changes with the term is the interest rate. The spot interest rate changes with the term, forming a mathematical curve of continuous fluctuation, which is called the yield curve.

It should be noted that the spot interest rate is not a market variable that can be directly observed, but an interest rate obtained by analyzing market data based on discounted cash flow method method.

Generally speaking, for a zero coupon with only one future cash flow, we can use yield to maturity as the spot interest rate for the corresponding period. If there are abundant zero coupon bond with various maturities in the market, it is easy for us to calculate the spot interest rate of each maturity, thus directly drawing the yield curve.

But in fact, all the zero-coupon tickets on the market are short-term. Only zero coupon can be used to calculate the shorter period of the yield curve. To make a complete yield curve, it is necessary to use various coupons with long term. This calculation involves some relatively complex mathematical models and algorithms, which cannot be completed manually.

Baidu encyclopedia-spot interest rate