# Question: You contribute 1 000 annually to a retirement account for 8

You contribute $1,000 annually to a retirement account for 8 years and stop making payments at the age of 25. Your twin brother (or sister . . . whichever applies) opens an account at age 25 and contributes $1,000 a year until retirement at age 65 (40 years). You both earn 10 percent on your investments. How much can each of you withdraw for 20 years (that is, ages 66 through 85) from the retirement accounts?

(Each of the previous problems may be readily solved using interest tables and financial calculators. There are, however, problems that are not easily solved using interest tables. For example, solving for the return on an investment that involves both an annuity and a single payment is a tedious process if you use interest tables. The same applies if the cash flows vary each year. However, a financial calculator may readily solve these problems.

Problems 28-30 illustrate this reality. All three are easily solved using a financial calculator but require that you employ a reiterative process when you are using interest tables. That is, you set up the equation and select a rate. If the results equate the two sides of the equation, you have solved the problem and determined the return. If not, you have to repeat the process until you have selected the rate that equates the two sides. After doing a couple of these problems, you may decide that learning how to use a financial calculator or a program such as Excel is worth the effort.)

(Each of the previous problems may be readily solved using interest tables and financial calculators. There are, however, problems that are not easily solved using interest tables. For example, solving for the return on an investment that involves both an annuity and a single payment is a tedious process if you use interest tables. The same applies if the cash flows vary each year. However, a financial calculator may readily solve these problems.

Problems 28-30 illustrate this reality. All three are easily solved using a financial calculator but require that you employ a reiterative process when you are using interest tables. That is, you set up the equation and select a rate. If the results equate the two sides of the equation, you have solved the problem and determined the return. If not, you have to repeat the process until you have selected the rate that equates the two sides. After doing a couple of these problems, you may decide that learning how to use a financial calculator or a program such as Excel is worth the effort.)

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