In this Warm-Up, students practice writing an exponential expression for repeated interest calculations. To emphasize the exponential structure of compounded interest, they are prompted to write an expression before calculating a monetary value.
You owe 12% interest each year on a $500 loan. If you make no payments and take no additional loans, what will the loan balance be after 5 years?
Write an expression to represent the balance and evaluate it to find the answer in dollars.
The loan balance will be 500(1.12)5 or about $881.17.
Invite students to share their expressions. If not already brought up in students' responses, bring up the following two expressions:
Highlight that the first expression with the 1.12 written out five times makes explicit the five separate years over which the interest is compounded. The second expression is shorthand for the first and is more succinct.
Some students may find it difficult to write an expression because they are reasoning about the interest calculation in additive terms, for example, 500+(0.12)⋅500 for the first year, [500+(0.12)⋅500]+(0.12)⋅[500+(0.12)⋅500] for the second year, and so on. Encourage them to think about each year's calculation as a product and to refer to the work in a previous lesson, if needed.
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In this Warm-Up, students practice writing an exponential expression for repeated interest calculations. To emphasize the exponential structure of compounded interest, they are prompted to write an expression before calculating a monetary value.
You owe 12% interest each year on a $500 loan. If you make no payments and take no additional loans, what will the loan balance be after 5 years?
Write an expression to represent the balance and evaluate it to find the answer in dollars.
The loan balance will be 500(1.12)5 or about $881.17.
Invite students to share their expressions. If not already brought up in students' responses, bring up the following two expressions:
Highlight that the first expression with the 1.12 written out five times makes explicit the five separate years over which the interest is compounded. The second expression is shorthand for the first and is more succinct.
Some students may find it difficult to write an expression because they are reasoning about the interest calculation in additive terms, for example, 500+(0.12)⋅500 for the first year, [500+(0.12)⋅500]+(0.12)⋅[500+(0.12)⋅500] for the second year, and so on. Encourage them to think about each year's calculation as a product and to refer to the work in a previous lesson, if needed.