Question

The U.S. government offers to sell you a bond for $362.45. No payments will be made until the bond matures 15 years from now, at which time it will be redeemed for $1,000. What annual interest rate would you earn if you bought this bond for $362.45?

a. 7.35%
b. 6.32%
c. 7.72%
d. 6.65%
e. 7.00%

Answer 1

The annual interest rate for a bond bought at $362.45 and redeemed for $1,000 after 15 years is approximately 7.72%, which corresponds to option (c). The interest rate is calculated using the future value formula for an investment.

Step-by-step explanation:

The question involves calculating the annual interest rate of a bond. To do this, we can use the formula for the future value of an investment, which is FV = PV(1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. In this case, the bond will pay $1,000 at maturity, so FV is $1,000, PV is $362.45, and n is 15 years. We need to solve for r.

By plugging the numbers into the equation and solving for r:

1000 = 362.45(1 + r)^15

We need to isolate r, which involves the 15th root and then subtracting 1. To solve for r, we use a financial calculator or software to get an approximate interest rate.

Therefore, the annual interest rate you would earn if you bought this bond for $362.45 is approximately 7.72%, which corresponds with option (c).