Formulas for Compound Interest After t years, the balance, A, in an account with principle and annual interest rate is given by the following formulas: For n compoundings per year: A = P(1 + r/n)nt . For continuous compounding: A = Pert. *continuous compounding is an infinitely small interval of time taken an infinitely large number of times per year.  Click for the first formula and explain to students that savings institutions have plans in which interest is paid more than once a year. Some plans allow for compounding every 6 months, some every 3 months, and even some every month. In general, when compounding interest is paid n times a year, we say that there are n compounding periods a year. Click for the second formula and explain that some banks use continuous compounding, where the number of compounding periods increases infinitely (every trillionth of a second, every quadrillionth of a second, etc).

Example First choice: Second choice: A = P(1 + r/n)nt A = Pert You decide to invest $8,000 for 6 years and you have a choice between two accounts. The first pays 7% per year, compounded monthly. The second pays 6.85% per year, compounded continuously. Which is the better investment? First choice: A = P(1 + r/n)nt = 8000(1+ 0.07/12)12(6) ≈ $12,160.84 Second choice: A = Pert = 8000(e0.0685(6)) ≈ $12,066.60 Read the question through to the students. Ask what investment they think will be the best before solving the problem. Click to work out the solution for the first choice. Before showing students the formula ask them what it is. Then click to reveal. Click to show what to plug into the formula. Click again to reveal the answer. Click to work out the solution for the second choice. Then ask students which is the better choice and click to reveal.