Don G
 |
The Par Value of a bond is the same as its Face Value, and Bonds always mature at that amount. A $1,000 Bond will pay $1,000 when it matures.
A $1,000 Bond, with a coupon rate of 10%, paid semi annually, with a 10 year life, will yield $1,213.19 today, if the market rate is 7%. Using a financial calculator, FV = 1,000. PMT (the Annuity) = $50 (Par Value x Coupon rate x 1/2). Number (of Payments) = 20. Rate = 3.5%. PV = $1,213.19
The proceeds of $1,213.19 are used to buy Bonds (with a Face or Par Value of $1,000) paying 6%, semi annually, for 8 yrs. The market rate is still 7%. So the Present Value of a $1,000 Bond (its Future Value), with a semi annual payment (the Annuity) of $30, Number of payments = 16, Rate = 3.5% amounts to $939.53. That's what you would pay today for one $1,000 Bond. If you invest $1,213.19, the so-called par or face value of your purchase will be in the same ratio as a $1,000 purchase.
So $1,000 is to $939.53 as x is to $1,213.19. Solve for x.
1000 / 939.53 = x / 1213.19; Cross multiply to get 1,213,190.00 = 939.53x ; Divide 1,213,190 by 939.53 to get $1,291.27, which is the Par Value, or Face Value, of the purchase.
A very difficult problem to follow, but it means that by investing $1,213.19 today at 7%, compounded semi annually, with semi annual interest payments of $38.74 (i.e. 3% of Par, or 1,291.27) for 8 Yrs, you will receive 1,291.27 at maturity. |
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