Bond Equivalent Yield Question

Exactly one year ago, an investor purchased a $1,000 face value, zero-coupon bond with 11 years remaining to maturity. The YTM was 8.0%. Now, one year later, with market rates unchanged, an investor purchaes an annuity that pays $40 every six months for 10 years. The combined value of the two investments based on the 8% BEY is approximately A. $966 B. 1,000 C. 1,007 D. 1,456 The correct answer is B, but I can’t figure how to set this problem up. A little help would be much appreciated.

I believe this has been solved before. Inv 1: FV=1000 N=20 PMT=0 I/Y=4 PV = 456.39 Inv 2: PMT=40 N=20 I/Y=4 PV = 543.61 Total = 1000 Choice B

i apologize for the repost and thanks for the help

Also, you can do this one without a calculator. From the zcb you have a $1,000 payment in 10 years’ time From the annuity you have $40 every 6mths for 10 years What is this the same as? A 10 year, semiannual pay 8% bond! Therefore with a market rate of 8%, the price must be “par”, or $1,000.