21.4 A Model for Saving - Video
- 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.