Derive and use the finite geometric series formula to solve problems such as mortgage-payment models.
Find the equal periodic payment from a finite geometric series model
Problem
What periodic payment is needed for this situation? You want to save \(5000\) in \(24~\text{months}\) at monthly factor \(1.004\) with end-of-month deposits.
Equal end-of-period deposits share one unknown multiplier, so first express their accumulated values at the target date and factor that payment amount outside the geometric sum. The earliest deposit grows for one fewer period than the number of deposits, and the last grows for zero. Once the sum is in closed form, divide the target by that entire accumulation factor.
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