Time Value

Time Value of Money

Future Value is the amount to which a payment or series of payments will grow over a given period when compounded at a given interest rate. Compounding is the process of going from present values to future values. Sample formula: FV= P x (1+i)n

While the present value is the value today of a future payment or series of payments discounted at the appropriate discount rate Discounting is the process of finding the present value of a payment or a series of future cash flows; the reverse of compounding. Sample formula: PV=P x 1/(1+i)n

Solving for Required Interest Rate or Time

Given a present sum of money and a desired future value, one can determine either the interest rate required to attain the future value given the time span, or the time required to reach the future value at a given interest rate. Because solving for the interest rate or time is slightly more difficult than solving for future value, there are a few methods for arriving at a solution:

1. Iteration - by calculating the future value for different values of interest rate or time, one gradually can converge on the solution.

2. Financial calculator or spreadsheet - use built-in functions to instantly calculate the solution.

3. Interest rate table - by using a table such as the one at the end of this page, one quickly can find a value of interest rate or time that is close to the solution.

4. Algebraic solution - mathematically calculating the exact solution.

Annuity is defined as a series of payments of an equal or constant amount of money at fixed intervals for a specified number of periods. The ordinary annuity are payments occur at the end of each period. Sample Formula: FV of OA = P x (1+i)n-1/i ; PV of OA = P x 1 [1/(1+i)n]/ i

Present Value of mixed stream

 Mixed flows

To compute the present value of a mixed stream, a spreadsheet is invaluable. Consider this problem, where cash flows vary and discount rates change according to the length of...