# Time and Value

time and value of money

How does compounding work as a lump sum of money grows over time?
Compound interest is interest that is earned not only on the principal investment, but on interest as well. As the interest rate rises, the compounding effect gets larger and larger through time.
   How can we find today’s value of a future lump sum?
To find the present value of a lump sum, we determine how much we would have to start with in order to end up with the future lump sum if we could earn i% interest for n time periods. This present value gets smaller as n increases and as the discount rate increases.
   How can we handle multiple cash flows that are not equal?
The key to handling an uneven cash flow series is to either compound or discount each cash flow separately. Only when they are evaluated at the same point in time can we add the values of these cash flows together.
   What is an ordinary annuity and how can its value be determined either now or at some future point in time?
An ordinary annuity is a series of equal payments where each payment is made at the end of each time period. We can find both the present value and the future value of ordinary annuities very efficiently by utilizing the PMT key on a financial calculator.
   What is the difference between an ordinary annuity and an annuity due?
An annuity due is also a series of equal payments, but each payment is made at the beginning of each time period. The simplest adjustment to account for differences in the present or future value of an annuity due from an ordinary annuity is to change the calculator settings to beginning of time period payments from ending payments. If you are receiving the payments, it is better to have an annuity due (an extra period of interest can be earned). If you are making the payments, ordinary annuities are better for you.
   How do we adjust for nonannual compounding periods?
For nonannual compounding we adjust the interest rate from the quoted, annual rate...