Question

In early April 2020 Australian 15-year government bonds were trading at a yield-to-maturity of 1.10% p.a., compounding semi-annually. The bonds have a coupon rate of 2.75% p.a., paid semi-annually. Suppose that in one year’s time 15-year Australian Government bonds (also with a coupon rate of 2.75% p.a., paid semi-annually), are trading at a yield-to-maturity of 1.60% p.a., paid semi-annually. The percentage change in the price of 15-year government bonds over this one year will be

Select one:

a. 3.1%

b. 6.1%

c. 5.1%

d. 4.1%

Answer 1

> Formula

P0 = Coupen Amount * PVAF (r, n) + Face Value * PVIF (r, n)

where PVAF = Present Value Annuity Factor

           PVIF = Present Value interest factor

> Calculation

Po = [ ( 2.75% / 2 ) * 1000 ] * PVAF (1.1% / 2, 15*2) + 1000 * PVIF (1.1%/2, 15*2)

      = 13.75 * [ 1/1.0055 + 1/1.00552 + .....+ 1/1.005530 ] + 1000 * [1/1.0055]30

      = 13.75 * 27.586 + 1000 * 0.8483

      = $ 1227.61 Answer

P1 = [ ( 2.75% / 2 ) * 1000 ] * PVAF (1.60% / 2, 15*2) + 1000 * PVIF (1.60%/2, 15*2)

      = 13.75 * [ 1/1.008 + 1/1.0082 + .....+ 1/1.00830 ] + 1000 * [1/1.008]30

      = 13.75 * 26.5776 + 1000 * 0.7874

      = $ 1152.84 Answer

Change in price = [ P1 - P0 ] / P0 * 100

                       = [ 1152.84 - 1227.61 ] / 1227.61 * 100

                       = 6.1% Answer

Hope you understand the solution.