Question
Charleston Independent School District needs to raise $200 millionto refurbish the existing schools and build new ones. Thebonds will pay interest semiannually at a rate of 7% per year, andthey will mature in 30 years. Brokerage fees associatedwith the sale of the bonds will be $1 million. If theinterest rate in the marketplace rises to 8% per year, compoundedsemiannually, before the bonds are issued, what will the face valueof the bonds have to be for the school district to net $200million? even if you can set up the solution, it would be great any help would be great, will rate lifesaver even if you justset up the solution even if you can set up the solution, it would be great any help would be great, will rate lifesaver even if you justset up the solution
Explanation / Answer
First off, I think you have to figure the total amountyou'll be paying for the brokerage fee + interest, using: Final amount = InitialAmount *(1 + r / n)nt Final = $1,000,000 (1+ .08 /2)2t where t = 30 years,assuming you're waiting to pay off this loan when the bonds comedue. Final = $10,519,627 The way bonds work is, you buy a "$200 million" bond for lessthan that, and at the maturity date, you can redeem them for thefull $200 million. Except that you alsowant to pay off the 10 million loan that has accrued, so the facevalue of the bonds that you need will total $210, 519,627 Finalamount = Initial Amount *(1 + r /n)nt Let's callinitial amount x. $210,519,627 = x (1 + .07 /2)2*30 Hope this makes sense... Then just evaluate the paretheses and raise it to the 60thpower. Then divide both sides by that amount so the x is leftalone. Let me know if you need any morehelp!