Present value, future value, and compounding made easy

Background

A dollar received now is more valuable than a dollar received a year from now. If you have that dollar today, you can invest it and increase its value. Let's explain a bit further:
The time of value of money is the difference in value between having a dollar in hand today and receiving a dollar sometime in the future.
Why is present and future value important?
Since money has a time value, we must take this time value into consideration when making business decisions. Present and future value calculations are powerful methods available in making financial decisions.
Once you understand and master the calculations, you can apply these equations for restating cash flows to make them equivalent in business decisions. The calculations are building blocks for many decisions facing individuals and managers alike. In addition, these calculations allow one to calculate returns on investments, capital budgeting, and return on annuities, just to name a few.

Key terms:

Future value (fv) and present value (pv) are two concepts in clarifying the value of money.
Future value is explained as an amount of money invested at present and will mature at the end of a given time when compounded at a given interest rate.
Present value is money that must be invested now to accrue to a certain amount of money in the future when compounded. In simpler terms, present value is the value today of an amount of money in the future. Why is this important? For these situations, businesses need to find a method of weighing cash flows that are received at various periods of times (annual, years, quarters, ect).

How do we go about finding the present and future value of cash flow?
There are two fundamental equations that are commonly used; this video will demonstrate them throughout the presentation.

Objectives:

Following my discussion, you will be able to:
• Have the knowledge of present value (pv) and future value (fv)
• Be able to calculate the pv and fv with compounding
• Have an understanding of compound interest
Discussion:

The video discusses the value of a dollar in hand today and applying calculations to determine what that dollar will be worth in the future. In addition, the video demonstrates the concept of wanting to have a specified amount of money in the future and the amount of money needed today in order to earn that specified amount.
See the formulas used in video:
Fv=pv (1+i) n
Pv= (1/1+i) n
FvPvn
Pv=the beginning amount
i= the interest rate/year
n=number of years
Fv=value at the end of n years.

Important points:

When computing compounding interest for greater than one year, remember that the interest in the next year is being paid on interest. The interest on the original dollar amount is referred to as "simple interest." Lastly, Net present value can be defined as the difference between the PV of cash inflows and the present value of cash outflows. Net present value is used in capital budgets to assess the probability of a project. The net present value is a standard affirming that a project should be established.
Example:
If a bank pays 5% interest on a $100 deposit today, in one year, this $100 will be worth $105. This is expressed by the following equation: F1= p (1+r). F1 is the balance at the end of the period, p represents the amount of invested, and r represents the rate of interest.

For example, the future of $1,000 compounded at 10%, would be $1,100 after one year and $ 1,331 after three years of investing. For example, if the interest rate is 10%, then the present value of $500 earned or spent in one year from now is $500 divided by 1.10, equates to $455. This example demonstrates the overall notion that the present value of a future amount is less than the actual future amount.
Summary

Present and future values are important methods for any financial decision. An investment can be viewed in two methods. We discussed present and future values in this video. The process of finding the present value of future cash flows is referred as discounting. Discounting future value to present value is a common technique, especially when weighing in on capital budget decisions. Have the knowledge of the calculations will allow individuals to calculate almost any investment decision

[mardi]

Thank you for this video. I appreciate the examples and speed of your explanations. I will do well on my Managerial Economics mid-term exam because of your video help.

[gacald]

This video helped me completely understand PV and FV. Thank You!!

[hsakailpop]

PV and FV and compounding are very clear now. Thank You!

[harnishkaur]

At the beginning of every month, Maggie invests $150 in an account with 6% annual rate. How much money will be in her account after 6 years?

please answer this question ASAP. I need it urgently

[renruida]

Great Video, really helps me understand the whole scenario

[DanaAPlant]

@5:17 you say it is better to take the 100 now and invest it with an interest rate of 5% but after one year that 100 is then 105 compared to the one year delay and getting 110? For some reason I can't understand why you think 105>110 or 100>104.76?

[prabakaranfxavier]

Thanks it’s great video, this help me a lot to understand the basic formula.

[agnesschungu]

If Maggie invests $1000, at 5% interest per year how much will be the future value be if t is unknown

[mehmetdogu]

many people learned this wrongly but yours correct.

[liquidpebbles]

this video was beautifully constructed

[k-mehrenworthallrightsrese]

Here today gone tommorow.. recoup, compute, value, invest, interest, Tender, IF THEN

[b]

i  watched 3 videos and they couldn't help me but you did so thank you. 

[hemantken]

A Machine will cost Rs. and will provide an annual net cash flow of Rs. 30, 000 for six years. The cost of capital is 15 % calculate machines NPV & IRR. Should the machine be purchased?
how to solve

[mosesberedugo]

some examples u gave are some how confusin... WELL, NICE WORK AND TNX FOR SHARING UR KNOWLEDGE WIT US

[simonclearwater]

if i invested $2000 each month for 3 years @ 3.85% interest compounding monthly - how would i calculate what id have 3 year's?

[PeakinDuckMusic]

@ 4:48, you say we divide the 110 by the interest rate. However, you are dividing the 110 by 1.05....the interest rate is not 105%. Can you clarify this?

[yudissubedi]

Show me how you calculate 3 years, 20 years etc in a simple calculator or by calculating. It's not clear.

[bMoreAK]

why would i take the $100 now if I am only going to make only $105 on my own. I would just wait one year and take $110. So why would u say it would more beneficial if I take the $100 now?
 

[mhassanyussuf]

Thanks a lot

But i have a new challenge.

How much do I have to save monthly to reach my target amount.
Take into account that the interest compounded yearly and interest is accrued daily.

Given
Target Amount (150000)
Start date (Always today)
End date (10-10-2030)
Interest(2, 30%)

[raaaft]

What happens if I have a deposit of let's say 1500 and then made deposits of 500. How would I calculate the final interest as the 1500 amount would also be compounded