Formulas from finance

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Section B.4 Formulas from finance

Compound Interest Formula

\begin{equation*} a = p \left( 1 + \frac{r}{12}\right) ^{12y} \end{equation*}

\(a\) = account balance ($)
\(y\) = time invested (years)
\(p\) = initial deposit or “principal”
\(r\) = interest rate compounded monthly (as a decimal)

Equivalent APR Formula

\begin{equation*} \text{APR} = \left(1+\frac{r}{12}\right)^{12}-1 \end{equation*}

where \(r\) = interest rate compounded monthly (as a decimal)

Future Value Annuity Formula

\begin{equation*} a = p \ast \frac{\left( 1 + \frac{r}{12}\right) ^{12y}-1}{\frac{r}{12}} \end{equation*}

\(a\) = account balance ($)
\(y\) = time invested (years)
\(p\) = regular (monthly) deposits ($)
\(r\) = interest rate compounded monthly (as a decimal)

Loan Payment Formula

\begin{equation*} p = \frac{a \ast \frac{r}{12}}{1-\left( 1 + \frac{r}{12}\right) ^{-12y}} \end{equation*}

\(a\) = loan amount ($)
\(y\) = time invested (years)
\(p\) = regular (monthly) payment ($)
\(r\) = interest rate compounded monthly (as a decimal)

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