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"Investment" Word Problems (page 1 of 2) Investment problems usually involve simple annual interest (as opposed to 深圳超1.68万套房源被锁 或陷旧改市场危情), using the interest formula I = Prt, where I stands for the interest on the original investment, P stands for the amount of the original investment (called the "principal"), r is the interest rate (expressed in decimal form), and t is the time.

For annual interest, the time t must be in years. If they give you a time of, say, nine months, you must first convert this to 9/12 = 3/4 = 0.75 years. Otherwise, you'll get the wrong answer. The time units must match the interest-rate units. If you got a loan from your friendly neighborhood loan shark, where the interest rate is monthly, rather than yearly, then your time must be measured in terms of months.

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In all cases of these problems, you will want to substitute all known information into the "I = Prt" equation, and then solve for whatever is left.

• You put \$1000 into an investment yielding 6% annual interest; you left the money in for two years. How much interest do you get at the end of those two years?

In this case, P = \$1000, r = 0.06 (because I have to convert the percent to decimal form), and the time is t = 2. Substituting, I get:

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I will get \$120 in interest.

Another example would be:

• You invested \$500 and received \$650 after three years. What had been the interest rate?

For this exercise, I first need to find the amount of the interest. Since interest is added to the principal, and since P = \$500, then I = \$650 – 500 = \$150. The time is t = 3. Substituting all of these values into the simple-interest formula, I get:

150 = (500)(r)(3)
150 = 1500r

150/1500 = r = 0.10

Of course, I need to remember to convert this decimal to a percentage.

I was getting 10% interest.

The hard part comes when the exercises involve multiple investments. But there is a trick to these that makes them fairly easy to handle.   Copyright © Elizabeth Stapel 1999-2011 All Rights Reserved

• You have \$50,000 to invest, and two funds that you'd like to invest in. The You-Risk-It Fund (Fund Y) yields 14% interest. The Extra-Dull Fund (Fund X) yields 6% interest. Because of college financial-aid implications, you don't think you can afford to earn more than \$4,500 in interest income this year. How much should you put in each fund?"

The problem here comes from the fact that I'm splitting that \$50,000 in principal into two smaller amounts. Here's how to handle this:

 I P r t Fund X ? ? 0.06 1 Fund Y ? ? 0.14 1 total 4,500 50,000 --- ---

How do I fill in for those question marks? I'll start with the principal P. Let's say that I put "x" dollars into Fund X, and "y" dollars into Fund Y. Then x + y = 50,000. This doesn't help much, since I only know how to solve equations in one variable. But then I notice that I can solve x + y = 50,000 to get y = \$50,000 – x.

THIS TECHNIQUE IS IMPORTANT! The amount in Fund Y is (the total) less (what we've already accounted for in Fund X), or 50,000 – x. You will need this technique, this "how much is left" construction, in the future, so make sure you understand it now.

 I P r t Fund X ? x 0.06 1 Fund Y ? 50,000 – x 0.14 1 total 4,500 50,000 --- ---

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 I P r t Fund X 0.06x x 0.06 1 Fund Y 0.14(50,000 – x) 50,000 – x 0.14 1 total 4,500 50,000 --- ---

Since the interest from Fund X and the interest from Fund Y will add up to \$4,500, I can add down the "interest" column, and set this sum equal to the given total interest:

0.06x + 0.14(50,000 – x) = 4,500
0.06x + 7,000 – 0.14x = 4,500

7,000 – 0.08x = 4,500

–0.08x = –2,500

x = 31,250

Then y = 50,000 – 31,250 = 18,750.

I should put \$31,250 into Fund X, and \$18,750 into Fund Y.

Note that the answer did not involve "neat" values like "\$10,000" or "\$35,000". You should understand that this means that you cannot always expect to be able to use "guess-n-check" to find your answers. You really do need to know how to do these exercises.