### The Relationship Between Present and Future Value

Present value (PV) and future value (FV) measure how much the value of money of money is "worth" at a specified time in the future assuming a certain interest rate for inflation or other factors that affect the true value of money in the future. Time value associated with money; Determining future value at given interest rate ; Present PVIFA = Annuity Factor = {1 – [1 ÷ (1+i)n] ÷ i} The relationship between the Present Value of a single amount and the Present Value of an Annuity. FV = Future Value of a dollar; P = Principal or Present Value; r = interest rate per year Take this product, the interest factor, and multiply it by the principal.

For example, bonds can be readily priced using these equations. A typical coupon bond is composed of two types of payments: The two formulas can be combined to determine the present value of the bond.

An important note is that the interest rate i is the interest rate for the relevant period. For an annuity that makes one payment per year, i will be the annual interest rate. For an income or payment stream with a different payment schedule, the interest rate must be converted into the relevant periodic interest rate.

For example, a monthly rate for a mortgage with monthly payments requires that the interest rate be divided by 12 see the example below.

See compound interest for details on converting between different periodic interest rates. The rate of return in the calculations can be either the variable solved for, or a predefined variable that measures a discount rate, interest, inflation, rate of return, cost of equity, cost of debt or any number of other analogous concepts. The choice of the appropriate rate is critical to the exercise, and the use of an incorrect discount rate will make the results meaningless.

For calculations involving annuities, you must decide whether the payments are made at the end of each period known as an ordinary annuityor at the beginning of each period known as an annuity due. If you are using a financial calculator or a spreadsheetyou can usually set it for either calculation. We can solve this problem in 2 ways.

In either case, we need to know how many compounding periods there are.

### Time value of money - Wikipedia

Since there is days to a year, there is 3, compounding periods in 10 years. Substituting these values into the IRD formula, the future value of the savings account is: Fluorescent bulbs don't pay interest!

You have a light bulb in your house, that's on quite a bit, and it's a watt bulb. You typically go through 13 bulbs in 5 years, for a total of 10, hours of light. But, what if you buy a watt fluorescent bulb, instead, which gives off almost the same amount of light, and it last 13 times longer than a typical watt bulb. A watt fluorescent bulb can be bought for nearly the same price as the 13 incandescent bulbs. Yes, fluorescent bulbs are more expensive than incandescents, but wait!

## The Present Value and Future Value of Money

So what is the equivalent interest rate that is compounded annually of this? Your only small risk is that the bulb breaks or turns out to be defective, in which case, you can probably return it to the store for another one.

Granted, these savings aren't going to allow you to buy a Lamborghini for your next car, but it's something that not only saves you money, but saves you time as well, since you won't have to change the bulb 12 times during those 5 years!

Multiply that by the number of bulbs in your house. Or if you have a business! Even a small business like a medical center could have a hundred or more light bulbs which are on all day during business hours. The savings could be quite substantial. Not only that, but you help to conserve energy and protect the world from global warming! Since this money is earned free of all taxes, we can also calculate a taxable equivalent yield.