Question

One year ago Lerner and Luckmann Co. issued 15-year, noncallable, 7.5% annual coupon bonds at their par value of $1,000. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 14 years to maturity?

Answer 1

Answer:

current price = $1191.79

Explanation:

given data

time t = 15 year

annual coupon bonds rate =  = 7.5 %

par value = $1000

interest rate = 5.5%

maturity time  = 14 year

to find out

current price of the bonds

solution

we get here first annual coupon rate = 7.5% of 1000

annual coupon rate  C = $75

so now we get current price of bond

current price of the bonds = $\frac{C}{(1+r)} +\frac{C}{(1+r)^2} +\frac{C}{(1+r)^3} +\frac{C}{(1+r)^4} ..........\frac{C}{(1+r)^{13}} + \frac{C+par\ value}{(1+r)^{14}}$      .................1

put here value

current price = $\frac{75}{(1+r)} +\frac{75}{(1+r)^2} +\frac{75}{(1+r)^3} +\frac{75}{(1+r)^4} ..........\frac{75}{(1+r)^{13}} + \frac{75+1000}{(1+r)^{14}}$  

current price = $\frac{75}{(1+r)} \frac{1-(\frac{1}{1+r})^{14} }{r} (1+r) + \frac{1000}{(1+r)^{14}}$

solve it we get

current price = $1191.79