Let’s see … $400 … enough for a pretty nice television, or a weekend at a really good hotel, or …

This, I imagine, is how most people will react if they’re lucky enough to get the $400-per child checks that will show up in 25 million mailboxes during the next few weeks.

The checks are an advance payment representing the increase, from $600 to $1,000, in the child tax credit for 2003. The boost was part of the federal tax cut approved last spring. It will go to low- and moderate-income taxpayers who claimed the credit on their 2002 returns.

(Those who are eligible this year but did not claim the credit for 2002 will be able to claim it when they prepare their 2003 returns next year. If you get a check and it turns out you aren’t eligible this year, it’s a windfall — the government won’t ask for the money back.)

I suspect a lot of these checks will be treated as windfalls and blown.

But what would be the best use for this money, if one had the self-control?

First and foremost — paying off high-rate credit-card debt. Getting rid of debt that’s costing you 15 percent a year is like earning 15 percent, guaranteed. You can’t beat that these days.

Next, of course, comes savings and investment. If you had a stock mutual fund that would return an average of 7 percent a year over the long run, $400 could turn into more than $1,500 over 20 years.

Also, remember this is just the first installment. The extra $400 credit applies to 2004, and could well become permanent.

So suppose you have two children and realize $800 a year for 10 years.

With a 7 percent annual return, you’d have more than $23,000 after 20 years. That’ll pay for a stack of great vacations after you retire.

How bonds work

Several readers asked for more detail on the subject of my column about how bond prices move up and down as interest rates change, so here goes.

As I said, when prevailing interest rates rise, bond prices fall, and vice versa.

Suppose you’d paid $1,000 for a bond carrying an interest rate of 3 percent, or $30 a year, and wanted to sell it. If new bonds were paying 4 percent, no one would pay a full $1,000 for your older bond. How much would they pay?

To illustrate the principle, I pointed out that the price would fall until that $30-per-year payment equaled 4 percent of the price. That would be $750, since $30 is 4 percent of $750. At this price, the old bond would offer the same yield as the new one.

In practice, other factors would affect the price. One of the most important is how long the bond has until it matures — the point at which the bond issuer repays the $1,000 principal. Interest-rate changes have a bigger effect on bonds with many years to maturity than on ones maturing soon.

Obviously, if a $1,000 bond were maturing tomorrow, a buyer wouldn’t care if interest rates jumped today. The bond would be worth $1,000, since that’s what its owner would get from the issuer tomorrow. With no more interest payments to be received, it wouldn’t matter if rates had gone up, down or stayed the same.

But if the bond investor would have to wait 30 years to get the $1,000 back, he’d be very leery of buying a bond carrying a rate lower than he could get on newer bonds. Over 30 years, a 3 percent bond would pay $900 in interest, while a 4 percent bond would pay $1,200. The difference would be even greater if the interest payments were invested and compounded.

Figuring how these factors affect bond prices takes math that’s beyond most of us. Fortunately, we have computers for that.

Take a look at the bond calculator at the Motley Fool Web site at www.fool.com/calcs/calculators.htm.

If you bought a $1,000, 30-year bond paying 3 percent and rates immediately rose to 4 percent, the bond would be worth only $823. If you had 10 years to maturity, the price would fall to $916. But if the very same bond were maturing in one year, the price would only fall to $989. (If rates fall, the opposite happens — the high-rate bond rises in price.)

A 1-point rise in interest rates would have less effect if rates started out higher. Your $1,000, 30-year bond would fall to $902 if rates rose from 9 percent to 10 percent — only half the loss you’d suffer in the rise from 3 percent to 4 percent.

Basically, this is because the 1-point rise in rates isn’t as damaging when the starting point is high. The 9 percent, 30-year bond will pay $2,700 in interest, the 10 percent bond $3,000. Locking in at 9 rather than 10 percent reduces interest earnings by 10 percent, while locking in at 3 instead of 4 percent cuts earnings by 25 percent.