17. Eighteen years ago when your maternalgrandmother passed away, she bequeathed

Question

17. Eighteen years ago when your maternalgrandmother passed away, she bequeathed to you 52 Merrill Lynchbonds. Since that time your parents have been investing the couponsin an account that yields 6.84%. Assuming the bonds and the accountyour parents have for you are all that you have, how much will yoube worth altogether, on the day the bonds mature?

The coupon for the bond is 6.875% and it matures April 2018. Thedate we're starting from is December 21st 2009. It seems to be afuture value of an annuity problem but every calculation I've donehas came out wrong. She gives us the answer of ($175,115.16) but Idon't know how to get it.

If you could help me it would be greatly appreciated.

Explanation / Answer

No of Bonds = 52 Face value FV of Bond = $1000 Coupon rate = 6.875%. So INT = 6.875%*1000 = 68.75 Int rate i = 6.84% Fractional period of days from 21 Dec to 30 Apr in year of maturity= approx 100days. So fractional year = 100/365 = 0.274 So Period n = 18Yr 100 days = 18.274 yrs Now Future value of annuity FVA = No of Bonds * INT*((1+i)^n-1)/i +Maturity value of 52 bonds ie FVA = 52*68.75*((1+6.84%)^18.274 - 1)/6.84%) + 52*1000 ie FVA = 52*68.75*(2.3503/6.84%) +52000 ie FVA = 52*2362.32 + 52000 = $174,841 approx

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