Final answer:
The annual return of a zero coupon bond purchased at $469 with a $1000 par value and 13 years until maturity is approximately 8%, which is calculated using the compound interest formula for zero coupon bonds.
Step-by-step explanation:
The question you've asked pertains to the calculation of the annual return from a zero coupon bond. To find this return, you're essentially trying to calculate the rate at which the investment grows annually from its purchase price to its par value over a set period of time, in this case, 13 years.
To calculate this, you would use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount (initial deposit or loan amount)
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per year
- t is the number of years the money is invested or borrowed for
As zero coupon bonds pay no interest until maturity, in this case we use n = 1 for annual compounding. We then solve for r as follows:
1000 = 469(1 + r)^13
Reducing it to:
(1 + r)^13 = 1000 / 469
Calculate the right-hand side:
(1 + r)^13 = 2.13198
Now we find the 13th root of 2.13198:
1 + r = 1.0809
Subtract 1 from both sides:
r = 0.0809 or 8.09%
Hence, the correct answer is not specifically listed among the options A) 7% B) 6% C) 5% D) 4% E) 3%, but it highlights