. If you purchase a zero coupon bond today for $225 and it matures at $1,000 in 11 years, what rate of return will you earn on that bond (to the nearest 10th of 1 percent)?
Excel spreadsheets are very helpful for these types of problems.
225*(1+r)^11 = 1000.
solve for r
(1+r)^11 = 1000/225 = 4.444
Raise 4.444 to the (1/11) power
I get r=.145
To calculate the rate of return on a zero coupon bond, we can use the formula for compound interest:
Rate of return = (Future value / Present value)^(1/n) - 1
Where:
- Future value is the maturity value of the bond ($1,000).
- Present value is the purchase price of the bond today ($225).
- n is the number of years until maturity (11).
Let's plug in these values into the formula:
Rate of return = (1000 / 225)^(1/11) - 1
Calculating this expression, we get:
Rate of return ≈ 0.0764
To express this rate as a percentage, we multiply by 100:
Rate of return ≈ 7.64%
Therefore, the rate of return on the zero coupon bond is approximately 7.64%.
To calculate the rate of return on a zero coupon bond, you can use the formula for yield to maturity (YTM). The YTM is the rate of return earned on a bond if it is held until maturity.
In this case, the zero coupon bond is purchased for $225 and matures at $1,000 in 11 years.
First, let's calculate the YTM step-by-step:
1. Determine the discount or premium: Subtract the purchase price from the face value to find the discount or premium. In this case, it is $1,000 - $225 = $775 discount.
2. Calculate the YTM: To find the YTM, divide the discount or premium by the purchase price and divide it by the number of years to maturity. Finally, express it as a percentage.
YTM = (Discount / Purchase Price) / Number of Years to Maturity
YTM = ($775 / $225) / 11
YTM ≈ 3.82 or 3.8% (rounded to the nearest 10th of 1 percent)
Therefore, the rate of return on the bond is approximately 3.8% (to the nearest 10th of 1 percent).