SAT Prep 2023 For Dummies with Online Practice by Ron Woldoff

Author:Ron Woldoff [Woldoff, Ron]
Language: eng
Format: epub
ISBN: 9781119886815
Publisher: Wiley
Published: 2022-05-26T00:00:00+00:00

It’s exactly the same as the simple interest formula, only the t exponent stands for time, usually counted in years. Note that this variation exists only on the SAT. Real interest compounds more often, so that formula looks like this:

where n is the number of times per year that the interest compounds. For example, if the interest compounds monthly, the formula looks like this:

The i is divided by 12 because it’s the annual interest divided monthly. The is because the interest compounds 12 times per year. The t in this case still represents years.

Note that n represents the number of times that the interest compounds during the time that i interest accumulates. If the interest rate is monthly, say 0.6% per month (which is 0.006), and the interest compounds once per month, then i isn’t divided by 12 and t isn’t multiplied by 12: The formula would look like , showing a monthly cycle that accumulates i interest.

Here’s an example. See if your understanding is sufficient to answer the question:

The money in a savings account increases 0.8% each month. Which of the following equations shows the future value, FV, of the money in the account based on the present value, PV, after a period of m months?

(A)

(B)

(C)

(D)

It’s not a math problem, remember. It’s a puzzle. Say you start with $100, so . If i is 0.8 percent, then use 0.008 (because , per Chapter 10). Which equation would lean in the direction of after the first month? Don’t do a lot of math. Instead, estimate and eliminate. If you have two or more answers that seem close, then do the math. But you won’t.

Choice (A): . No matter what m is, this won’t lead to $100.80, so cross it off.

Choice (B): . If m is 1, as it would be after the first month, then this leads to $100.80. Leave it — if you need to calculate further, you can always come back and do so.

Choice (C): . Not a chance. Run it through your calculator with (in other words, the first month) and you’ll see why.

Choice (D): . This is closer, but here’s the thing. Because the denominator is slightly more than 1, each month the value of the account goes down slightly, not up. If a swimming pool has a slow leak, this type of equation would model the diminishing amount of water.

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