Question

a. You own a 28-year, 4.1% annual coupon bond with $1,000 face value. If the yield to maturity is 5%, how much is it worth? Round to the nearest cent.

b. You make a one-time $2,604 deposit into an account which pays 2.6% compounded weekly. If you don't touch this account for 6 years, how much interest will the account generate during that time? Round to the nearest cent.

Answer 1

a)

Annual coupon = 4.1% of 1000 = 41

Price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price = 41 * [1 - 1 / (1 + 0.05)^28] / 0.05 + 1000 / (1 + 0.05)^28

Price = 41 * [1 - 0.255094] / 0.05 + 255.093637

Price = 41 * 14.898127 + 255.093637

Price = $865.92

Bond will be worth $865.92

b)

There are 52 weeks in a year

Number of periods = 6 * 52 = 312

Weekly rate = 2.6% / 52 = 0.05%

Future value = Present value (1 + rate)^time

Future value = 2,604 (1 + 0.0005)^312

Future value = 2,604 * 1.168781

Future value = $3,043.50

Total interest = $3,043.50 - $2,604

Total interest = $439.50