Question

Suppose that Ryan can buy bond A or bond B, both of which have face value of $1000. Bond a pays a 4% coupon rate annually in perpetuity, and Bond B pays an annual 10% coupon rate and matures in 1 year. Ryan is different between bond A and bond B. What is the real interest rate in this economy?

The answer is apparently 3.8%

How do you do this problem? I don't understand how they got the answer.

Answer 1

Let i be market interest rate

Bond 1

Coupon rate = 4%

Face value = 1000

pays coupon amount annually in perpetuity

coupon amount = 4% * 1000 = 40

Present value of future coupon payments = 40 / i

Bond 2

Coupon rate = 10%

Face value = 1000

pays coupon amount for 1 year and face value after 1 year

coupon amount = 10% * 1000 = 100

Total payment after 1 year = 1000 + 100 = 1100

Present value of bond = 1100 / (1+i)

As there is no difference between the two bonds, so present value must be equal,so

1100 / (1+i) = 40 / i

1100*i = 40 + 40*i

1060 * i = 40

i = 40/1060 = 0.037735 = 3.7735% = 3.8% (rounding off)