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"Investment" Word Problems (page 1 of 2)

Investment problems usually involve simple annual interest (as opposed to compounded interest), using the interest formula I = Prt, where I stands for the interest on the original investment, P stands for the original investment (called "principal"), r is the interest rate, and t is time.

(Note that, for annual, that is to say, yearly, interest, the time t must be in years. That is, if they give you a time of, say, nine months, convert this to ⁹/₁₂ = ³/₄ = 0.75 years. Otherwise, you'll get the wrong answer. The same requirement holds true for other time units. If it's a monthly interest rate from the local loan shark, time must be in terms of months; etc. Note also that these problems are not terribly realistic; in "real life", interest is pretty much always compounded somehow, and investments are not generally all for just one year. But you'll get to more "practical" stuff later; this is just warm-up, to prepare you for later.)

In all cases of these problems, you will want to substitute all known information into the "I = Prt" equation, and solve for whatever is left. For simple problems, this involves something like this:

• 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 (remember to convert from a percent to a number by moving that decimal point!), and t = 2. Substituting, I get:

I = (1000)(0.06)(2) = 120

I get $120 in interest.

Another example would be:   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

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

For this problem, I have P = $500, I = $650 – 500 = $150, and t = 3. Substituting, I get:

150 = (500)(r)(3)
150 = 1500r
¹⁵⁰/₁₅₀₀ = r = 0.10

Remember to convert this decimal to a percentage.

I was getting 10% interest.

The hard part comes when the problems involve multiple investments. But there is a trick to these that makes them do-able.

• 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, if x + y = 50,000, then 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!

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

Now I will show you why I set up the table like this. By organizing the columns according to the interest formula, I can now multiply across and fill in the interest column.

	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 get my equation:

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 problems.

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