Question

John needs $1,000,000 to retire in five years. There is an
annual zero-coupon bond that will mature in 8 years, that has a YTM
of 11.75%.

If John buys the bond and the YTM moves to 9.75% when he sells the
bond in 5 years, how much money will John have for retirement

If John buys the bond and the YTM moves to 13.75% when he sells the bond in 5 years, how much money will John have for retirement?

Answer #1

Jhon plans to purchase a zero coupon bond. These bonds do not have any coupon payment , instead they are Issued at Discount and Redeemed at par.

So the FV is 1,000,000

Time is 5 yrs.

Rate YTM = 11.75%.

So he will pay

PV = FV/(1+r)^n

Or

1,000,000/(1.1175)^5 = $ 573,802.37 for the bond.

Now in Case 1,

YTM goes to 9.75 he will be receiving

FV = 573802.37(1+0.0975)^5 = $ 913,660.78

In case 2

Ytm is 13.75

So jhon will get

FV = 573802.37(1+0.1375)^5= 1092746.36

Thanks

a zero-coupon bond with face value $1,000 and maturity of five
years sells for 946.22. Its YTM is

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