Question

Suppose 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

Answer: The answer is 7.53%

Step-by-step explanation:

To calculate for the discount rate of d(0,4)d(0,4)

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

Provided the interest rates are compounded annually the discount factor will give the present value of the bond when provided with the interest rate and maturity value.

Going with the above, 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 hence be 0.748.

Therefore, to calculate the discounting factor for the 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

Finally, the discount rate will be 7.53%