Simple Interest

[Anonymous]

Bill, a teacher at one of my schools asked if students need to memorize i=prt for our state assessment because it is not listed on the formula sheet students are allowed to use during testing.  When  I asked my advisors at the state dept, they suggest that I ask you.  They are thinking 7th graders will only have to determine interest when given a principle amount and a rate, or find one of the missing values when given the other two.  Will you please advise us further on this?

[Bill McCallum]

It seems this is a question for your state assessment writers, not for me! Or are you talking about the PARCC or SBAC assessment? I don’t think we know this level of detail about them yet. Anyway, here are some thoughts.

I guess you are talking about the following standard

7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

The thrust of the standard is problem solving using proportional relationships. It’s hard for me to imagine students working with lots of simple interest problems without ending up knowing that you calculate the annual interest by multiplying the principle by the annual interest rate and that you add that interest every year (or month or whatever time period you are using), leading to proportional relationship between the interest and the number of years. So, you might want students to be able to solve:

Write an equation expressing the relationship between the interest $I$ and the number of years $t$ if the principle is $\$500$ and the annual interest rate is 4%.

by first calculating the annual interest to be $0.04 \times \$500 = \$20$ and then using that information to come up with the equation $I = 20t$. You might do a similar problem where the number of years is given and the goal is to come up with a proportional relationship between $I$ and $P$. Or you might ask them to come up with a graph or a table.

Is this the same as knowing the formula $I=Prt$? Yes and no. One the one hand, a student who knows all this has all the ingredients to construct the formula. On the other hand, in Grade 7 you might want to stick to proportional relationships where only two of the quantities are represented by variables and the others are given constants, as in the problem above.

So, without knowing exactly what your teacher means by “memorize $I=Prt$,” it seems to me that it is starting out in the wrong place. If it means sticking the formula into your head without understanding what it means, then you might as well use a cheat sheet. And if you have worked lots of problems with simple interest then it’s hardly necessary to memorize it.

We want students to see formulas as useful ways of expressing relationships between quantities, not as black boxes that you plug numbers into.

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