Download Calculating Annuities: Paying In and Receiving Monthly Payments and more Study notes Mathematics in PDF only on Docsity! January 29 Annuities An annuity is a repeating payment, typically of a fixed amount, over a period of time. An annuity is like a loan in reverse; rather than paying a loan company, a bank or investment company pays you the monthly payment. 2 Paying into an Annuity Suppose you need to have $100,000 saved 20 years from now. If you can invest at 6% per year, how much do you need to put away each month? Each monthly investment will be collecting interest; the earlier payments will collect more. 5 If P is your monthly investment, r the monthly return rate, and m the number of months you invest, then the amount of money you will have after m months is P * ((1 + r)m - 1) r F = 6 If you know how much you will need to have, you can solve this formula for how much you need to invest each month: P = ((1 + r)m - 1) F * r 7 This is the same formula as for loans, because an annuity is really a loan in which you are the lender. 10 Question If you have invested $200,000 and receive an annual rate of return of 7%, how much will you receive each month if you get payments for 20 years? What if you want payments for 30 years? What about for 40 years? 11 Answer Using the loan formula, the values are: $1550.60 a month for 20 years $1330.60 a month for 30 years $1242.86 a month for 40 years 12 Entering in a Spreadsheet You can enter a formula with numbers more or less as they would be written in these slides. However, you can also use variables. We’ll look at examples of each. 15 To calculate 100 * (1 + .05/12)240, you can type = 100 * ( 1 + .05 / 12 ) ^ 240 in a cell. You will get 271.26 (rounding to two places) 16 You can use cell references for variables. Each entry is determined by a column and a row. An example of a cell reference in Excel is B4; this refers to column B and row 4. 17 Summary of Interest Rates • Compound Interest • Inflation • Loans • Paying into an Annuity • Collecting from an Annuity 20 F = P * (1 + r)n where, F = future amount P = principal (initial investment), r = interest rate (converted to decimal) n = number of years Compound Interest 21 If P is the present value of money, at an inflation rate of r% per year (made into a decimal), the equivalent value n years later is F = P * (1 + r)n Inflation 22
