When the money is loaned or borrowed for a longer time period, if the interest is paid (or charged) not only on the principal, but also on the past interest, then we say the interest is compounded. If...When the money is loaned or borrowed for a longer time period, if the interest is paid (or charged) not only on the principal, but also on the past interest, then we say the interest is compounded. If an amount \(\mathrm{P}\) is invested for \(t\) years at an interest rate \(r\) per year, compounded \(n\) times a year, then the future value is given by \[A=P\left(1+\frac{r}{n}\right)^{n t} \nonumber \] \(\mathbf{P}\) is called the principal and is also called the present value.
