solve the formula a = \\frac{p\\left\\left(1 + \\frac{r}{n}\\right)^{nt}-1\\right}{\\left(\\frac{r}{n}\\right…

Explanation:

Step1: Multiply both sides by $\frac{r}{n}$

$A\times\frac{r}{n}=P\left[\left(1 + \frac{r}{n}\right)^{nt}-1\right]$

Step2: Divide both sides by $\left[\left(1+\frac{r}{n}\right)^{nt}-1\right]$

$P=\frac{A\times\frac{r}{n}}{\left(1 + \frac{r}{n}\right)^{nt}-1}=\frac{Ar}{n\left[\left(1+\frac{r}{n}\right)^{nt}-1\right]}$

The formula $A=\frac{P\left[\left(1+\frac{r}{n}\right)^{nt}-1\right]}{\frac{r}{n}}$ is the future - value of an ordinary annuity formula, where $A$ is the future value of the annuity, $P$ is the payment amount per period, $r$ is the annual interest rate (in decimal form), $n$ is the number of compounding periods per year, and $t$ is the number of years. The resulting formula $P=\frac{Ar}{n\left[\left(1+\frac{r}{n}\right)^{nt}-1\right]}$ describes the payment amount per period $P$ of an ordinary annuity given the future value $A$, annual interest rate $r$, number of compounding periods per year $n$, and number of years $t$.

Answer:

$P=\frac{Ar}{n\left[\left(1+\frac{r}{n}\right)^{nt}-1\right]}$; It describes the payment amount per period of an ordinary annuity.