Question

How to find compound interest quarterly?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{general}\mathrm{formula}\mathrm{for}\mathrm{the}\mathrm{amount}\left(\mathrm{A}\right)\mathrm{incurred}\mathrm{on}\mathrm{a}\mathrm{principal}\mathrm{amount}\left(\mathrm{P}\right) \\ \mathrm{at}\mathrm{R}\mathrm{percent}\mathrm{compounded}\mathrm{annually}\mathrm{for}\mathrm{n}\mathrm{years}\mathrm{is}\mathrm{given}\mathrm{by}, \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ \mathrm{In}\mathrm{case}\mathrm{the}\mathbf{interest}\mathbf{}\mathbf{is}\mathbf{}\mathbf{compounded}\mathbf{}\mathbf{quarterly},\mathrm{then}\mathrm{we}\mathbf{divide}\mathbf{}\mathbf{rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{interest}\mathbf{} \\ \mathbf{by}\mathbf{}\mathbf{4}\mathrm{and}\mathbf{multiply}\mathbf{}\mathbf{time}\mathbf{}\mathbf{n}\mathbf{}\mathbf{by}\mathbf{}\mathbf{4}\mathrm{so}\mathrm{that}\mathrm{it}\mathrm{becomes}, \\ {\mathrm{R}}_1=\frac{\mathrm{R}}{4}\%\mathrm{per}\mathrm{quarter} \\ {\mathrm{n}}_1=4\mathrm{n}\mathrm{quarters} \\ \mathrm{Now}\mathrm{calculate}\mathrm{amount}\mathrm{using}\mathrm{P},{\mathrm{R}}_1\mathrm{and}{\mathrm{n}}_1 \\ \mathrm{By}\mathrm{subtracting}\mathrm{the}\mathrm{principal}\mathrm{amount}\mathrm{P}\mathrm{from}\mathrm{the}\mathrm{amount}\mathrm{A},\mathrm{we}\mathrm{can} \\ \mathrm{get}\mathrm{the}\mathrm{desired}\mathrm{compund}\mathrm{interest}. \end{gathered}$$