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A-SSE.4 Warmup M3-017-A06-V01

Derive and use the finite geometric series formula to solve problems such as mortgage-payment models.

Build a finite geometric-series model for a loan balance after repeated end-of-period payments

Problem

Write the loan-balance model after \(6\) end-of-period payments for principal \(1000\), periodic growth factor \(1.01\), and payment \(100\).

Neutral loan cash-flow timeline showing principal $1000 at time zero and six equal negative $100 end-of-period payments through valuation after payment 6; the model formula is withheld. Open full size
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What this problem is really about

Build a loan balance by valuing every cash flow at one common date. The original principal begins at time zero and grows through every period, while end-of-period payments accumulate over progressively fewer periods, ending at exponent zero. Because payments reduce what is owed, their geometric-series value is subtracted from the grown principal.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-SSE.4
Category
Algebra
Domain
Seeing Structure in Expressions
Objective
Derive and use the finite geometric series formula to solve problems such as mortgage-payment models.
Problem type
Build a finite geometric-series model for a loan balance after repeated end-of-period payments