Problem 7: Future Value of Annuities

Josephine, age twenty-two, started working full-time and plans to deposit $3,000 annually into an IRA that earns 6 percent interest. How much will be in her IRA in twenty years? Thirty years? Forty years?

To solve this problem, clear your calculator's memory and set the number of payments to one (for an annual payment). Set I equal to six and the PMT equal to $3,000.

• For twenty years: Set N equal to 20 and solve for FV. FV = $110,357
• For thirty years: Set N equal to 30 and solve for FV. FV = $237,175
• For forty years: Set N equal to 40 and solve for FV. FV = $464,286

If Josephine increased her return rate to 10 percent, how much money would she have after each of the three time periods? How does this interest rate compare to the 6 percent interest rate over time?

Do the previous problems at 10 percent interest. Begin by clearing the calculator's memory. Set I equal to ten and the PMT equal to $3,000.

• For twenty years: Set N equal to 20 and solve for FV. FV = $171,825 (This is $61,468 more than she would earn at the 6 percent interest rate)
• For thirty years: Set N equal to 30 and solve for FV. FV = $493,482.07 (Josephine would earn $256,307.51 more than at the 6 percent rate)
• For forty years: Set N equal to 40 and solve for FV. FV = $1,327,777.67 (Josephine would earn $863,491.77 more than at the 6 percent rate)

Your rate of return and the length of time you invest make a big difference when you retire.