Question

Suppose you bought a bond with an annual coupon of 7 percent one year ago for $1,010. The bond sells for $985 today.

a.Assuming a $1,000 face value, what was your total dollar return on this investment over the past year?
b.What was your total nominal rate of return on this investment over the past year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
c.If the inflation rate last year was 3 percent, what was your total real rate of return on this investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

(a) $45

(b) 4.45%

(c) 1.4%

Explanation:

Given that,

Value of bond one year ago = $1,010

Annual coupon rate = 7%

Selling value of bond today = $985

Face value = $1,000

(a) Total dollar return on this investment:

= Current bond price - Last year price + Coupon payment

= $985 - $1,010 + ($1,000 × 7%)

= $985 - $1,010 + $70

= $45

(b) Nominal rate of return on this investment:

= [(Current bond price - Last year price + Coupon payment) ÷ Last year price]

=  [($985 - $1,010 + ($1,000 × 7%)) ÷ $1,010]

= $45 ÷ $1,010

= 0.0445 or 4.45%

(c) Inflation rate last year = 3%

Total real rate of return:

= [(1 + Nominal rate) ÷ (1 + Inflation rate)] - 1

= [(1 + 4.45%) ÷ (1 + 3%)] - 1

= 1.0140 - 1

= 0.0140 or 1.4%