21.4 A Model for Saving - Video

Key Ideas

  • A geometric series with first term 1, common ratio x, and n terms is the following 1 + x + x2 + . . . + xn-1 and the sum of these terms is (xn - 1)/(x -1) where x is never 1.
  • We can accumulate a desired amount of money in a savings account by a fixed date by making regular deposits at regular intervals—a
  • sinking fund. With a uniform deposit of d dollars at the end of each interval and an interest rate of i per interval, the savings formula predicts that the value of the account after n intervals.
  • An annuity is a sinking fund in which the same amount is deposited regularly.
  • In order to solve for the amount to be deposited in an annuity directly, we can solve the savings formula for d to find the payment formula.