Question

uppose the current term structure of interest rates, assuming annual compounding, is as follows: s_1s 1 ​ s_2s 2 ​ s_3s 3 ​ s_4s 4 ​ s_5s 5 ​ s_6s 6 ​ 7.0% 7.3% 7.7% 8.1% 8.4% 8.8% What is the discount rate d(0,4)d(0,4)? (Recall that interest rates are always quoted on an annual basis unless stated otherwise.)

Answer 1

7.53%

Step-by-step explanation:

Calculation for the discount rate of d(0,4)d(0,4)

The discount factor is : d=1/1+i

And given that the interest rates are compounded annually the discount factor will gives the present value of the bond when provided with the interest rate and maturity value.

Therefore the present value of a bond with a maturity value of 1 will be;

Present value=1 /(1+i1) (1+i) (1+i3) (1+i4)

Present value=1 / (1.07) (1.073) (1.077) (1.081)

Present value=0.748

The present value of a bond with a maturity value of 1 will therefore be 0.748.

Now, let calculate the discounting factor for the whole 4 years:

1 (1+d (0,4))‐⁴ =0.748

(1+d(0,4))=0.748‐¹/⁴

1+d (0,4) =1.0753

d (0,4)=0.0753

Therefore the discount rate will be 7.53%