 Have you ever wondered how much a dollar today will be worth in five, ten, or twenty years? Every penny that you spend has an opportunity cost. If you would’ve saved this money instead, it could’ve multiplied into massive savings toward your financial goals. That is why it’s so important to make sure that you are paying as little in interest as possible. Make a point of paying off your debt and saving more money.

For those of you who love math, this article gives a brief overview of time value of money concepts using real-life examples. Specifically discussed are the future value of a single sum, present value of a single sum, future value of annuities, present value of annuities, serial payments, and net present value. The article also touches on how NPV and IRR can be used by businesses for investment purposes.

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A dollar that is received today is worth more than a dollar that is received two years from today. Why? It’s because the dollar that is received today can be invested and will be worth more in two years.

Here are two basic terms that you should know regarding time value of money:

1. Future value is the future dollar amount that a sum today will increase with a compounded defined interest rate and a period of time.

2. Present value is the current dollar value of a future sum that is discounted at a defined interest rate and a period of time.

## An Example on Future Value of a Single Sum

Any money you earn today will be worth more next year than it is right now.

For example:

LiWei has an account that's valued at \$100 today and is paying 10% interest compounded annually. The future value at the end of year 1 is the present value multiplied by 1 plus the interest rate. This would mean that Liwei’s account will earn \$10 interest. He will have \$110 at the end of the year.

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## Present Value of a Single Sum

The calculation for present value is used to determine what a sum of money to be received in a future year is worth in today’s dollars on a specific discount rate.

Here’s the formula: Future Value ÷ {(1+i)^n}

## Future Value of Annuities

An annuity is a series of equal payments at fixed intervals for a specified number of periods. If the payments are at the end of each period, they are called an ordinary annuity (usually mortgage payments). However, If the payments are made at the beginning of each period, they are referred to as an annuity due (usually lease or rent payment).

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## Present Value of Annuities

The difference between the present value of an annuity due and the present value of an ordinary annuity is that ordinary annuity due’s payments are made at the beginning of each period rather than at the end, and the other way around for annuity due. Due to this, the present value of an annuity due is always larger than the present value of an ordinary annuity with the same payments. This calculation is used most often for education funding and for retirement needs analysis.

## Serial Payments

Serial payments are payments that increase at a constant rate on a regular basis. There are many situations where it can be more affordable to increase payments on an annual basis because the individual expects to have increases in cash flows or earnings to make those increasing payments.

Serial payments differ from fixed annuity payments because the payments are not a fixed amount every year. Because of this, the initial serial payment is less than its respective annuity payment. The last serial payment will obviously be greater than the last respective fixed annuity payment. However, the last serial payment will have the same purchasing power as the first serial payment.

Serial payment is calculated by using an inflation-adjusted interest rate formula: {[(1 + r) ÷ (1 + i)] – 1} × 100

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## An Example of Net Present Value (NPV)

Net present value analysis is a method used by businesses and investors to evaluate capital projects and capital expenditures. In order to calculate the net present value, you would start with the amount and timing of future cash flows, including the projected future sale of the investment. These cash flows are then discounted by a certain rate of return, and the resulting is a present value of future cash flows. Adding the purchase price against this figure will allow you to arrive at the asset’s net present value.

For example:

If the present value of a series of cash inflows is \$300 and the initial outflow is \$250, the NPV becomes \$50 (\$300 – \$250).

An NPV that is greater than zero means that the initial rate of return of the cash flows is greater than the discount rate used to discount the future cash flows.

An NPV of zero implies that the discount rate used is equal to the initial rate of return for the cash flows.

A negative NPV implies that the discount rate used is greater than the true IRR of the cash flows.

As a general rule, looking for investments that have a positive NPV is advisable. The initial rate of return is a measure of an investment rate of return (IRR). It is the discount rate that makes the present value of the cash inflows equal to the initial cash outflows to make the net present value equal to zero.

NPV is considered to be superior to IRR when comparing investment projects with unequal lives. NPV helps a company decide whether to buy a particular piece of equipment or make a particular investment. The result of NPV calculation is written in dollars and not a percentage. NPV equals the difference between the initial cash outflow and the present value of discounted cash inflows.

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## Analyze Your Cash Inflows and Outflows for Improvements

The math doesn’t lie. Future cash is worth more than cash today. Don’t deplete your budget every month with unnecessary expenses, as the opportunity cost is too great. By utilizing time value of money calculations, you can motivate yourself to save more money. Whether you are self-employed or a company’s employee, let compound interest work for your financial goals.