# How does Value get rounded in figuring out Bonds Value?

I was reading up on Bonds here on About.com Why Do Bond Prices and Yields Move in Opposite Directions?

In the second example it offers:

In this example, the opposite scenario occurs. The same company issues Bond A with a coupon of 4%, but this time yields fall. One year later, the company can issue new debt at 3.5%. What happens to the first issue? In this case, the price of Bond A needs to adjust upward as its yield falls in line with the newer issue. Again, Bond A came to the market at \$1000 with a coupon of 4%, and its initial yield to maturity is 4%. The following year, the yield on Bond A has moved to 3.5% to match the move in prevailing rates (as reflected in the 3.5% yield on Bond B). Since the coupon stays the same, the price must rise to \$1142.75. Due to this increase in price, the yield declines (because the \$40 coupon divided by \$1142.75 equals 3.5%).

After reading the part I bolded, I tried to compute it on my own:

`40 / n = 3.5`
`40 / .035 = n`
`n = 1142.8571426`

However, they come up with 1142.75. From what I gather its ultimately a fluctuation based on market anyways. But I'd still like to know. If I reverse and do `40 / 1142.85` I get `0.03500021875` while `40 / 1142.75` yields `0.03500328155`. So how does one accurately round or compute this? Am I just missing something in my math?

• Significant digits may be an idea to consider here as the 4% and 3.5% are only 1 or 2 significant digits. Both the values you give would round to 3.500% at 3 or 4 significant digits you do realize right? – JB King Jul 14 '14 at 6:00
• @JBKing yes I saw that which is why I'm asking the correct way to round, which could be with significant digits. – Ender Jul 14 '14 at 13:46