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Homework answers / question archive / 1) Consider a zero−coupon bond with a? $1000 face value and 14 years until maturity

1) Consider a zero−coupon bond with a? $1000 face value and 14 years until maturity

Finance

1) Consider a zero−coupon bond with a? $1000 face value and 14 years until maturity. If the YTM of this bond is? 7%, then the price of this bond is $________

2) Carlyle plans to make month-end contributions of $400 to his RRSP from age 20 to age 40. From age 40 to age 65, he plans to make no further contributions to his RRSP. The RRSP can earn 9% compounded annually from age 20 to age 60, and then 5% compounded annually from age 60 to age 65. Under this plan, what is the maturity value of his RRSP when he turns 65?

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1) We can calculate the price of bond by using the following formula in excel:-

=-pv(rate,nper,pmt,fv)

Here,

PV = Price of bond

Rate = 7%

Nper = 14 periods

Pmt = 0

FV = 41,000

Substituting the values in formula:

= -pv(7%,14,0,1000)

= $387.82

2) We can calculate the amount at age 40 by using the following formula in excel:-

=fv(rate,nper,-pmt,pv)

Here,

FV = Amount at age 40

Rate = 9%/12 = 0.75% (monthly)

Nper = 20*12 = 240 periods (monthly)

Pmt = $400

PV = $0

Substituting the values in formula:

= fv(0.75%,240,-400,0)

= $267,154.75

 

We can calculate the amount at age 60 by using the following formula in excel:-

=fv(rate,nper,-pmt,pv)

Here,

FV = Amount at age 60

Rate = 9%/12 = 0.75% (monthly)

Nper = (60-40)*12 = 240 periods (monthly)

Pmt = $0

PV = $267,154.75

Substituting the values in formula:

= fv(0.75%,240,0,-267154.75)

= $1,605,373.36

 

We can calculate the maturity value by using the following formula in excel:-

=fv(rate,nper,-pmt,pv)

Here,

FV = Maturity value

Rate = 5%

Nper = 65-60 = 5 periods

Pmt = $0

PV = $1,605,373.36

Substituting the values in formula:

= fv(5%,5,0,-1605373.36)

= $2,048,908.42

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