Problem preview

A-SSE.4 Warmup M3-017-A08-V02

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

Find how many periods are needed in a finite geometric-series model

Problem

For a loan balance modeled by \(L\cdot~b^n~-~P(b^n~-~1)/(b~-~1)\), what inequality and logarithm expression determine the number of whole periods needed for the balance to be at most \(0\)? Assume \(b~>~1\) and \(P~>~L(b~-~1)\).

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bⁿ >= P/(P + L(b - 1)); n >= log(P/(P + L(b - 1)))/log(b), then round up

bⁿ >= P - L(b - 1); n >= log(P - L(b - 1))/log(b), then round up

bⁿ = P/(P - L(b - 1)); n = log(P/(P - L(b - 1)))/log(b), then round up

bⁿ >= P/(P - L(b - 1)); n >= log(P/(P - L(b - 1)))/log(b), then round up

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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: Find how many periods are needed in a finite geometric-series model