Question

Redesigned Computers has 9 percent coupon bonds outstanding with a current market price of $896.23. The yield to maturity is 10.34 percent and the face value is $1,000. Interest is paid semiannually. How many years is it until this bond matures

Answer 1

16 years to maturity

Step-by-step explanation:

We will calculate time:

The bonds present value is 896.23

YTM 10.34

and the face value is 1,000

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

Coupon Payment: 45 (1,000 x 9% / 2 payment per year)

time n

rate 0.0517 (10.34/2 payment per year

`45 * (1-(1+0.0517)^(-n) )/(0.0517) = PV\\`

PVc

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time n

rate 0.0517

`(1000)/((1 + 0.0517)^(n) ) = PV`

PVm

PV c + PV m = 896.23

`45 * (1-(1+0.0517)^(-n) )/(0.0517) + (1000)/((1 + 0.0517)^(n) ) = 896.23`

We rearrenge:

`(1-(1+0.0517)^(-n))* (45)/(0.0517)+(1+0.0517)^(-n) * 1,000 = 896.23`

We solve to clear the expression 1.0517 power -n:

`870.4061896 - 870.4061896(1.0517)^(-n)) + 1000(1.0517)^(-n) = 896.23`

`129.59(1.0517)^(-n) = 896.23 - 870.4061896`

`(1.0517)^(-n) = 25.82381044 / 129.59`

We now use logarithmics properties:

`log0.20 / log1.0517 = -n`

n = 32.00

These are semianual payment, so we will divide by two to get the time expressses in years:

32/2 = 16 years to maturity