If you purchase a zero coupon bond today for 225 and it matures at 1000 in 11 years, what rate of return will you earn on that bond?
Please show formula and answer
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 you earn if you hold the bond until it matures.
The formula for YTM is:
YTM = ((Face Value / Purchase Price)^(1/n)) - 1
Where:
- Face Value is the amount the bond will be worth at maturity (1000 in this case).
- Purchase Price is the amount you paid for the bond (225 in this case).
- n is the number of years until maturity (11 in this case).
Let's plug in the values and calculate the YTM:
YTM = ((1000 / 225)^(1/11)) - 1
Calculating this equation, we get:
YTM = (4.44) ^ (1/11) - 1
Using a calculator, we find that (4.44) ^ (1/11) is approximately 1.1573.
Therefore, the YTM is:
YTM = 1.1573 - 1
YTM = 0.1573 or 15.73%
So, the rate of return you will earn on this zero coupon bond is 15.73%.