How to Calculate the Present Value of an Annuity

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In this video, I show how to calculate the present value of an annuity. In addition to converting the series of payments via the traditional discounting method, I'll show how to solve the problem utilizing a handy equation.

[@kylelane630]

Thanks for this! I learn much better in videos, rather than just reading :)

[@NickD956]

Been learning Quantitative Measures chapter in my Investment Management Certificate. This helped alot! very easy to follow and much preferred to the book description. thanks!!! (guy who hasn't touched this sort of math since leaving school 7 years ago)

[@jcuempire]

I am glad I found this! I was agonizing over this concept. You explained it perfectly. Thanks very much!

[@Moe27777]

Thank you very much!! I finally understand what I was doing wrong.

[@preciousntobeng328]

Thank you for step by step calculation on the PV of interest

[@cadettipk]

I've seen 2 other videos on this concept and this one actually made it stick. I'm definitely going to ace this part of my test now. Thanks!

[@Alanisbusinessacademy]

That's awesome! Good luck!

[@hestycho]

Thank you so much! you teach me better than my teacher haha

[@firestar8538]

Thank you!! My homework got easier.

[@Alanisbusinessacademy]

Jonathan Owens That's great! Glad I could help.

[@smithjo4152]

Thank You so much Matt for the rapid response. Just so I could understand, to determine real cash flows and real discount rates, do I reduce these items by the inflation rate and based on your previous response, am I merely subtracting the inflation rate from the cash-flow?

[@smithjo4152]

Thank You for these instructions. I have a question, How do you add the calculation of inflation to this equation?

[@naomyn2479]

woow. Thank you so much.....this is awesome indeed

[@chlarissamaeurbi5957]

very helpful! thank youuu!

[@Alanisbusinessacademy]

Absolutely. You would have to change the number of periods (n) and your interest rate (i). For example, if you were discounting future cash flows for 3 years, but in quarters, you would multiple that figure by 4 to get 12 periods. You would also modify your interest rate, lets say 8 percent annually, by dividing it the number of quarters in a year (4) to get 2 percent per quarter. Great question. Hope this helps.

[@smithjo4152]

Thank You Matt. I am in a MBA program and this is my 2nd to last class to complete the program. Next is econ. Ugh!. So I will be in contact with you in the future i am sure.... Are there instructional classes that I could sign up for that you offer? You are very good.

[@jimmynwakalor9139]

automatically my new favorite channel thanks a lot

[@Alanisbusinessacademy]

That's a huge honor. Thanks Jimmy!

[@crazycouplevideosin3minute382]

Thanks Man!!!

[@arbmv89]

¡GRACIAS! Very easy to understand.

[@Alanisbusinessacademy]

Andrew Vazquez You're very welcome. Thank you.

[@waynerisner4974]

Thank you

[@themissperfect89]

You are amazing! :D

[@Alanisbusinessacademy]

You're very kind. Glad I could help.

[@smithjo4152]

No Problem Matt. Thank You. This is a bit confusing. Is there a way for me to better understand this? So in summary, the interest rate has to be reduced by inflation? Thank You again Matt. This helps so much.....

[@Optimized_Finance.]

can the amount be discounted quarterly.. thanks for your vedio

[@mitchellhenning6411]

How would you calculate a PVA with more than one interest rate at a certain point in the future. For example for a 12 year annuity at 2900 each month and for the first 8 years the interest rate is 8% compounded monthly, but after the first 8 years the interest rate switches to 6% compunded monthly

[@varshneyabhushan]

thx !!!

[@joshuarobertdaniels]

How do I calculate, at the end of my payments, how much I can withdraw over a given period of time, while still collecting the original interest rate? The account balance at the end being zero.

[@SoloPro]

Thanksssssssssssssssssssssss!!

[@tasnimahmedchowdhury7287]

Thanks a lot!

[@Alanisbusinessacademy]

+Tasnim Ahmed Chowdhury You’re welcome!

[@noeudpapillon8432]

Thanks OBVIOUSLY

[@ruthdogani8745]

Thsnks for good teacher

[@ruthdogani8745]

Am understand how to calculate present value and annuity

[@lizjk4]

What happens to the present value of an annuity when the interest is compounded more frequently? Could you share an example to visualize it please? I can see from the timeline, the amount declines every year. My book says the value declines, but I'm getting confused because when I think of interest compounded more frequently I think of how the interest amount increases. Thanks

[@Alanisbusinessacademy]

Good question. I'm in the middle of a few projects so unfortunately I'm not available to record a separate video. Let me try to explain though. If you choose to compound interest more frequently (i.e. semi-annually, quarterly, monthly) then it will result in a higher future value and lower present value. This is because the process of compounding more frequently allows interest to accumulate more quickly. The process for determining the PV or FV when compounding more frequently is the exact same, however your "n" and "i" variables will change to account for the changing in compounding frequency. For example, if your annual interest rate is 8.0 percent, but you are compounding interest semi-annually, then you would use an interest rate of 4.0 percent because you're compounding twice in the year. Lets say that you wanted to determine the future value after four years of compounding interest at 8.0 percent annually. Since interest is compounded twice a year, and you have 4 years, you'll have a total of 8 periods (n=8). Hope this helps to clarify a bit.

[@chidieberekalu5034]

Pls I need a quick ans..what if in a loan the payment is paid twice a year yet compounded monthly

[@DrCashcow10]

are the annuities in this video and the one about future value annuity take into account interest or inflation or both, because i am confused on this

[@Alanisbusinessacademy]

DrCashcow10 I didn't touch upon this topic as the goal of this video was simply to introduce students to the formula. You could factor that into the equation yourself by reducing your interest rate by whatever value you believe inflation will be. Fro example, if you project the interest rate to be 6% while inflation holds at 1.5% than use 4.5% as i.

[@eshrn04102]

i don't get this, I thought that n should be in negative.

[@dineshsiva2491]

how did u get the formula?

[@emmanuelnartey8867]

How can I derive the interest rate of an annuity with growth rate ?

[@chaostodoroki7077]

thankyou

[@sattikiganguly544]

How would you derive the formula?

[@hansenzarael6957]

It derived from the fact that payment of 1 is made at the end or beginning of each year and hence you have (1)v+(1)v^2+.... and this will give u (1-v^n/i)

[@rumishruu7394]

Thanks

[@Alanisbusinessacademy]

No problem

[@harrisonwintergreen1147]

what represents the 8% commission?

[@bestgirlstar]

is n the number of years calculated?

[@dhairyajaiswal2423]

What would you do if there were compounding periods? like if the value was put in quarterly for 5 years, how would the i value and n value change?

[@Alanisbusinessacademy]

If you're compounding periods you would need to make changes to both the interest rate (i) and the number of periods (n). Divide your annual interest rate by four and then multiple the number of periods by 4. So you'll have 20 periods over 5 years if you're compounding quarterly.

[@hansenzarael6957]

please I badly want to know the difference between continuously payable cashflows and annuities

[@rayanrules]

Just wondering but how would you find out constant monthly payments of something, not during a specific time period like in this example? (i.e how much would someone have to pay monthly to pay off there debt in 10 years)

[@Alanisbusinessacademy]

That's a great question Ray. You will likely use an amortization schedule to determine the number of years needed to pay off a debt. The following equation will allow you to answer your question Payment = I x Amount/1 - (1 + I )-N. This of course will only look at the explicit cost and not take into account the time value of money. Hope this helps.

[@ashleytalkington2128]

How would you calculate the interest rate of the present value of an annuity?

[@suzannetegroen3791]

my teacher is a douche. He changed the formula on me and said instead of giving me the interest he left the percent out told me Ii had to find it. He gave 600 dollars it doubled in 9 years what is the annual interest. That was the problem and had no idea how to find the interest. Can you help me? My final is on Saturday December 10th 2017

[@joshuawrightwayjay]

Greeting got a question for you. Whenever I calculate 1.07 to the third power and divide by one i keep coming up with 1.225043 instead of .8162979. Can you help me understand why that is? Please and thank you.

[@Alanisbusinessacademy]

Hey there! Looks like you have the order of operations reversed. Instead of dividing 1.225 by 1, divide 1 by 1.225.

[@Me-ji2pn]

6:48 but you didnt show why it was that formula??

[@sporttimes3858]

R2'200 invested at a certain rate of interest increased by 110% after 60 months. Compute the Final Amount of the investment at the end of month 60.

[@rodjohns2550]

Can you show me how to use this formula and solve for i showing all the steps?

[@Alanisbusinessacademy]

Rod Johns If you remember back to your days in math class you'll use the order of operations. PEMDAS is the acronym to determine priority, which stands for parenthesis, exponents, multiplication, division, addition, and subtraction. Since there's nothing to solve in parenthesis you'll solve for the exponent first (1.07 to the 3rd power). Divide 1 by the result of 1.07^3. Then solve for 1 minus the result of your previous calculation (should be roughly .81629) which should be around .18370. Then take that figure and divide it by your interest rate, which is .07. Hope that helps.

[@rodjohns2550]

***** Thanks but i think you mistook what i was getting at. I know how to solve the equation as per your example, i.e. I have no problems entering the values into the equation and solving for PV. What I want to see is how to solve for the interest rate, i.e, set the equation up to solve for i (the interest rate). It's been along time since i have done math like this > I get as far as 1-PVi/M = 1/(1+i)^n. What are the final steps to get the equation to be set up to solve for r??

[@uzzy901]

how would you calculate the PV if let's say if £100 was invested from years 1-3 and 250 invested from years 4-6?

[@Alanisbusinessacademy]

Usmaan You can use one of three methods. The first is to discount those future cash flows by hand and then add all of them together. The second is to use a financial calculator and enter the cash flows into a cash flow register while solving for PV. The third is to use the corresponding formula in Microsoft Excel. I hope this helps.

[@zenoelea8613]

Usmaan Use the "Calculate Present Value Annuity Factor (PVAF) J to N" calculator here to do it: www.mrzeno.com/Present-Value-Annuity-Factor-PVAF.php Therefore, the answer, for a discount rate of 6% using your figures would be: £267.30 + £561.08 = £828.38

[@kondaiahpericherla1620]

How to come 1.07

[@kondaiahpericherla1620]

I dont no

[@klarc]

wow my book is beyond complicated

[@aishiteru6325]

Need solution for this T^T I don't understand how to solve this. "if payments of ₱5,000 are made every quarter for 10 years at 7% interest compounded quarterly."

[@jangzterrizer9405]

Period will be 4q times 10 years

[@AK-yj4nu]

doesn't the formula of PV have a negative n as power? so why is there a positive n as power?

[@Alanisbusinessacademy]

There are a few variations of the PV formula Alisha Walia Kaur. In order to use a negative exponent you would need to change the equation using some basic arithmetic to get the correct response. Perhaps I'm just an optimist and prefer a positive over a negative.

[@AK-yj4nu]

Ohhh, I get it. Thank you so much. Great video by the way. I referred it for my math exam that I had today and it really helped me. :)

[@Alanisbusinessacademy]

You're very welcome! Glad it helped.

[@blacksword6868]

with the example shown in the video, the exponent should still be positive, as you're only calculating the value of one payment for each period. the formula that has the negative exponent is the one that calculates the values of all payments.

[@Yan-wj6kz]

Indonesia☝️😂

[@Alanisbusinessacademy]

Yay for Indonesia!

[@DrCashcow10]

I still do not understand the difference between (future value of annuity) and present value

[@Alanisbusinessacademy]

DrCashcow10 The present value presents what a lump sum of money is worth today. The future value represents what a lump sum of money (today) is worth at some point in the future. An annuity is an equal stream of payments. A future value of annuity commonly represents something like a 401k or other retirement plan. Not only do you commonly invest a lump sum upon creation of the account, but you typically have money diverted from your paycheck each pay period as well. Hope this helps.

[@thegoatfelicia1]

this is really frustrating because my teacher gave a different formula with the same variables and i plug them into the formula my teacher gave us, and i get a different answer. ughghhghhghg

[@zenoelea8613]

The Goat Felicia This online calculator shows the step-by-step calculation in detail. Try plugging your numbers into this website and then compare against your own workings. It may help? www.mrzeno.com/Present-Value-Annuity-Factor-PVAF.php