Financial Bonds 500 $1,000 bonds with stated rate of 5% issued at par. 10 year term and pay interest semi-annually.

Question

Every time I try and calculate this problem something comes up wrong. Either from working it out by hand or using my BA II plus, I cannot get the answer shown below. Am I wrong or is this book answer off?

500 bonds at $1,000 with a stated rate of 5%.

The present value $500000,

payable in 20 six-month periods at a market rate of 5% is $305,135.47. But I cannot come up with that number, using a BA II plus caculator or doing the calculations by hand.

The present value of 12,500 of intrest (500000 x 5% interest / 2 payments per year) paid for 20 six-months periods at a market rate of 5% is 194864.53

Answer 1

Par value is the dollar amount that will be paid to the bondholder at maturity of the bond, i.e., in ten years. Interest does not actually accrue on the bond; rather, the prospective bondholder calculates what they should pay now for the bond, given the effective interest rate that they desire, which is 5% in this case.

So $500,000 is the future value (FV) of the bonds. Then, we can calculate the present value (PV) by the following:

$$ \mathrm{FV}=$500,000=\mathrm{PV}(1.025)^{20} $$

Solving for PV gives

$$ \mathrm{PV}=\frac{$500,000}{(1.025)^{20}}=$305,135.47 $$

Let me know if this makes sense or not.