If you purchased a zero coupon bond today for $225 and it maturity value is $1,000 in 11 years, what rate of return will you earn on that bond?
P = M/(1 + r)^n
P = price
M = maturity value
r = investor's required annual yield/2
n = number of years to maturity x 2
225 = 1000/(1 + r/2)^22
225(1 + r/2)^22 = 1000
(1 + r/2)^22 = 4.4444
take the 22nd root of each side
1 + r/2 = 1.07015
r/2 = 0.07015
r = .1403
r = 14%
check my math
Online calculators come up with a cost of 236.62 versus 225.00
Close enough because of rounding.
To calculate the rate of return on a zero coupon bond, you can use the formula for compound interest:
Rate of return = (Maturity value / Purchase price)^(1/Number of years) - 1
In this case:
Maturity value = $1,000
Purchase price = $225
Number of years = 11
Plugging the values into the formula, we get:
Rate of return = ($1,000 / $225)^(1/11) - 1
Calculating this expression will give you the rate of return on the bond.
To calculate the rate of return, also known as the yield to maturity, of a zero coupon bond, we can use the following formula:
Rate of return = (Maturity value / Purchase price) ^ (1 / Number of years) - 1
Let's put the values into the formula:
Maturity value = $1,000
Purchase price = $225
Number of years = 11
Now, we can substitute these values into the formula:
Rate of return = ($1,000 / $225) ^ (1 / 11) - 1
Now let's calculate it step by step:
Step 1: Division
Rate of return = 4.444 ^ (1 / 11) - 1
Step 2: Exponentiation
Rate of return = 1.344 - 1
Step 3: Subtraction
Rate of return ≈ 0.344
Therefore, the rate of return on this zero coupon bond would be approximately 0.344 or 34.4%.