Similar reasoning can be used when determining how much to save for
retirement. Suppose a person is 25 years of age now and plans to retire at
age 65. For the next 40 years they plan to invest a portion of their monthly
income in securities which earn interest at the rate of 10% compounded
monthly. After retirement the person plans on receiving a monthly payment
(an annuity) in the absolute amount of $1500. The amount of money the
person should invest monthly while working can be determined by equating
the present value of all their deposits with the present value of all their
withdrawals. The first deposit will be made one month from now and the
first withdrawal will be made 481 months from now. The monthly deposit
amount will be be denoted by the symbol x. The present value of all the
deposits made into the retirement account is