Calculate the yield-to-maturity of a zero-coupon bond that costs $650 today and will pay $1,000 at the end of five years. Round your answer to the nearest tenth of a percent.
A)8.6%
B)9.0%
C)5.4%
D)none of the above

Question

Quizplus · Accepted Answer

The yield-to-maturity (YTM) is the rate of return that an investor will earn if they hold the bond until maturity, assuming all interest payments are reinvested at the same rate. In the case of a zero-coupon bond, there are no interest payments, so the YTM is simply the discount rate that equals the present value of the bond to its face value.

Using the formula for present value of a future sum:
Present value = Future value / (1 + r)^n

Where r is the discount rate and n is the number of years until maturity.

Plugging in the values given:
$650 = $1,000 / (1 + r)^5

Solving for r:
(1 + r)^5 = $1,000 / $650
(1 + r) = (1,000 / 650)^(1/5)
(1 + r) = 1.087
r = 0.087 or 8.7%

Rounding to the nearest tenth, the answer is B) 9.0%. The yield-to-maturity can be calculated using the formula:
YTM = [(face value/present value)^(1/n)] - 1
YTM = [(1000/650)^(1/5)] - 1
YTM = 0.0898 or 8.98%
Rounding it to the nearest tenth gives us an answer of 9.0%, which is option B.

Calculate the Yield-To-Maturity of a Zero-Coupon Bond That Costs $650