A zero-coupon bond matures for $1,000 in exactly 12 years' time. If you paid $385.63 today for the bond, what average yearly rate of return will you earn?
I don't think I am right, but $83.33 or 32.13 I am b=not sure
Let r=interest rate
385.63*(1+r)12=1000
(1+r)12 = 1000/385.63 = 2.5932
Solve for 1+r and calculate r as the interest rate.
Quick check:
Rule of 72 says that money invested at r% will double in 72/r years (approximately).
Since the investment has more than doubled in 12 years, the interest rate should be more than 72/12=6%.
In fact, it is over 8%.
Post your results if you want to check.
To find the average yearly rate of return, we can use the formula for compound interest:
A = P(1 + r)^n
Where:
A = the future value (in this case, $1,000)
P = the present value (paid today, $385.63)
r = the interest rate
n = the number of years (12)
We can rearrange the formula to solve for the interest rate (r):
r = (A/P)^(1/n) - 1
Substituting the values into the formula:
r = (1000/385.63)^(1/12) - 1
Now, we can calculate the value of r to determine the average yearly rate of return.