Math 108 Topics in Mathematics | Laura Barnes |
21.4 A Model for Saving - Video

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 + x^{2} + . . . + x^{n-1} and the sum of these terms is
(x^{n} - 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 intervalsâ€”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.