Question

Solve the following question by using the excel sheet on your computer

If a bond pays $70 in one year and $140 in two years, its present value is $200. Find the interest rate which equates the price of the bonds with the future values discounted. Use in your experiment 10 interest rates (hint: start your calculation from interest rate =1%). Based on your results what is the relationship between the interest rate and the price of the bond?           

Answer 1

Let the interest rate is r%, then according to the facts provided, the discount future value @r% = $200

i.e. 200 = 70/(1+r%) + 140/(1+r%)^2

i.e. 200*(1+r)^2 = 70*(1+r)+140

i.e. 200+200*r*r + 400*r = 70 + 70*r + 140

i.e. 200*r*r + 330*r -10 = 0

r = [-330 + [ 330*330 - 4*200*(-10) ]^0.5] / 400 OR [-330 - [ 330*330 - 4*200*(-10) ]^0.5] / 400

r = -330 + 341.9 / 400 OR (-330 - 341.9) / 400

Ignoring negative amount, r = 0.029766 or r = 2.9766%

As the interest rate increases, price of the bond decreases.