Question

Suppose you bought a bond with an annual coupon rate of 8.3 percent one year ago for $906. The bond sells for $944 today.

If the inflation rate last year was 4.3 percent, what was your total real rate of return on this investment?

Answer 1

Step-1, Nominal Rate of Return on the Bond

Annual coupon amount = $83 [$1,000 x 8.30%]

Original Price of the Bond = $906

Change in Bond Price = $38 [$944 - $906]

Therefore, the Nominal Rate of Return on the Bond = [(Annual coupon amount + Change in Bond Price) / Original Price of the Bond] x 100

= [($83 + $38) / $906] x 100

= [$121 / $906] x 100

= 13.36%

Step-2, Real Rate of Return

The Real Rate of Return is calculated by using the following formula

Real Rate of Return = [(1 + Nominal Rate) / (1 + Inflation Rate)] – 1

Nominal Rate = 13.36%

Inflation Rate = 4.30%

Therefore, Real Rate of Return = [(1 + Nominal Rate) / (1 + Inflation Rate)] – 1

= [(1 + 0.1336) / (1 + 0.0430)] – 1

= [1.1336 / 1.0430] – 1

= 1.0869 – 1

= 0.0869 or

= 8.69% (Rounded to 2 decimal place)

“Hence, the total real rate of return on this investment = 8.69%”