Step-by-step explanation:
The rate of return on a zero-coupon bond can be calculated using the formula for yield to maturity (YTM). Since the bond is a zero-coupon bond, it does not pay periodic interest (coupons) but instead is purchased at a discount to its face value.
The formula for yield to maturity (YTM) on a zero-coupon bond is as follows:
YTM = [(Face Value / Current Price)^(1 / Number of Years to Maturity)] - 1
Where:
Face Value = the face value or maturity value of the bond ($1,000 in this case)
Current Price = the current market price of the bond ($280 in this case)
Number of Years to Maturity = the number of years until the bond matures (20 years in this case)
Now, let's plug in the values and calculate the rate of return (YTM):
YTM = [($1,000 / $280)^(1 / 20)] - 1
YTM = (3.571428571428571)^0.05 - 1
YTM = 1.0832829543 - 1
YTM = 0.0832829543
To express the rate of return as a percentage, we need to multiply it by 100:
Rate of Return = YTM * 100
Rate of Return = 0.0832829543 * 100
Rate of Return ≈ 8.33%
So, the rate of return on the $1,000 zero-coupon bond with a 20-year maturity, which is currently priced at $280, is approximately 8.33%.