Tutorials by Brand:
Lump Sum Formulas
These are the main formulas that are needed to work with lump sum cash flows (Definition/Tutorial).
I use MathJax to display these formulas. You can click the equations to show a zoomed version in a pop-up, or right-click on the formulas for additional options (e.g., to copy the equation as $\TeX$ or to choose the zoom settings).
| To Solve For: | Formula |
|---|---|
| Future Value | $$FV = PV{\left( {1 + i} \right)^N}$$ |
| Present Value | $$PV = \frac{{FV}}{{{{\left( {1 + i} \right)}^N}}}$$ |
| Number of Periods | $$N = \frac{{\ln \left( {\frac{{FV}}{{PV}}} \right)}}{{\ln \left( {1 + i} \right)}}$$ |
| Discount Rate | $$i = \sqrt[N]{{\frac{{FV}}{{PV}}}} – 1$$ |
| Variable | Definition |
|---|---|
| $$FV$$ | Future Value |
| $$PV$$ | Present Value |
| $$i$$ | Discount Rate per Period |
| $$N$$ | Number of Periods |
| $$Pmt$$ | Annuity Payment per Period |
| $$\ln{()}$$ | Natural Logarithm ($\log_e$) |