Time Value of Money Calculator

The time value of money is the idea that a dollar today is worth more than a dollar tomorrow because the money you have now can be invested to make a profit. This tool applies this concept to five variables common to all financial problems: present value, interest rate, number of periods, regular payments, and future value. Enter four of these known values into the fields below and leave the fifth field blank, then click "Calculate" for the missing value.

What is the time value of money?

Money has a time value because it can be invested to earn interest. If you put cash in a savings account or buy bonds, you will receive interest so that the same amount of money will have more purchasing power in the future than today. Extending this idea leads to the concept of future value and compound interest; reversing it gives the present value or discounting.

Almost every decision involving money is based on this relationship. Mortgages, car loans, credit cards, retirement accounts and even the value of bonds and companies can ultimately be traced back to moving money over time at a particular interest rate.

Five input parameters:

There are five variables in time value of money problems. If four of them are known, the fifth can be derived.

There are two settings that affect these inputs: the compounding frequency determines how often per year interest is calculated and paid out, while the timing specifies whether each payment is made at the beginning or end of its respective period.

Formula

For a lump sum with no payments, future value is calculated using a compound interest formula.

PV is the present value, r is the annual interest rate as a decimal, m is the number of compounding periods per year, and t is the number of years. Assuming an investment of $1,000, an interest rate of 6 percent, and a time period of 10 years with interest compounded annually, in this case r = 0.06, m = 1, and t = 10.

If fixed payments are also made at each period, these form an annuity. If the payments are made at the end of each period, then the amount increases as follows:

In the example above, adding $100 annually increases the future value to about $3,108.93. Of that, $1,000 is the initial principal amount, $1,000 are the ten payments and the rest is interest.

The difference between present value and future value.

Present value and future value are the result of looking at the same equation from two different perspectives. Future value asks what a present amount will be worth in the future with interest compounding. Present value asks what a future amount is worth today, discounted back to its present value.

This is why both can be processed with the same calculation tool. When you input a future value, the program will calculate compound interest for the future, and when you input a present value, it will discount it to its current worth. The rate of interest used in discounting is usually referred to as the discount rate or required rate of return.

In what situations is it useful?

You can predict savings balances, calculate how much you need to contribute to meet a goal or determine the interest rate required to reach a particular goal with an investment. You can input payments and calculate how much you must save each month to receive a certain amount in the future. You can input the number of years and check how long it will take for a particular balance to grow to a certain level. Ultimately, all plans can be reduced down to one of these five numbers so that different options with varying interest rates and terms can be compared on an equal footing.

Tips to make results more realistic:

Use an interest rate that you are comfortable with and avoid the most optimistic scenarios. Over long periods of time annual returns on broad equity indices have been about 7 to 10 percentage points before inflation so these numbers are a reasonable starting point for estimating growth. The frequency of compounding should match the account in question. For longer time frames turn on the inflation option and check the value of the result in current currency as purchasing power is more important than nominal book value.

This tool is for educational and planning purposes only and does not constitute financial advice. Returns are not guaranteed and actual results may vary depending on market conditions, taxes, fees, and various other costs. Please consult a qualified professional before making any investment decisions.