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Chapter 8: Problem 23

Solve for \(P\) : $$ A=\frac{P\left[(1+r)^{t}-1\right]}{r} . $$ What does the resulting formula describe?

Short Answer

Expert verified
The resulting formula, \(P = \frac{r \cdot A}{(1 + r)^t - 1}\), describes the amount of each payment (\(P\)) needed to accumulate a given future amount (\(A\)), over a certain number of periods (\(t\)), at a specific interest rate per period (\(r\)).

Step by step solution

01

Isolate P on One Side

To isolate \(P\), multiply the whole equation by \(r\): \[r \cdot A = P((1 + r)^t - 1)\]
02

Complete Isolation of P

Divide both sides by \(((1 + r)^t - 1)\) to get \(P\) by itself: \[P = \frac{r \cdot A}{(1 + r)^t - 1}\]

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