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
How many whole periods are needed to reach this target? Deposits of \(100\) grow according to the series \(100[(1.01)^n-1]/0.01\), and the total must be at least \(2000\).
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What this problem is really about
A target that must be reached calls for an inequality, not just an equation. Isolate the exponential power, use logarithms to find the threshold for the period count, and remember that time advances in whole periods. If the logarithmic result is not an integer, use the next whole period and verify the adjacent counts to confirm it is the first one that works.
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