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In this lesson, we show how to calculate interest rates using the financial calculator BA II PLUS Texas Instrument. We explain and go through examples of how to calculate interest rates when there is compounding using the financial calculator BA II PLUS Texas Instrument. We go through various examples with compounding annually (yearly), compounded quarterly, and compounding monthly. We also show how to calculate the interest rate when the payment compounding and interest rate compounding are different.

Welcome to contacts in this lesson we’re going to be looking at how to calculate interest rates using the financial calculator the ba2 plus texas instrument now we’ve done many other lessons using this financial calculator so you’ll find the links to all those lessons in the description below most of which are based on time value of money so let’s look at the

First one we are told here that if you invest 10 000 rent today in an account that will result in 14 500 grand in five years time what is the interest rate that is earned so here we are looking for the interest rate and if you see what we have we have the 10 000 rent which you’ll have to invest today that’s the present value and it will result in 14 500 rand

That is the future venue and the period day is five years so we’re going to use the time value of money element over here and we’re going to start from the left going all the way to the right putting in what we have and then computing what we need to calculate which is the interest rate in this particular examples so before we do that let’s make sure that we

Reset our calculator making sure that we don’t have any input calculations that will affect our answer so we press second function and then we press here it’s written plus slash minus and then it’s asking us if we want to reset you press enter and then you’ve just reset your calculator so you just press your c c to clear your screen now we can start with our

Calculation another thing to note here is that by default this financial calculator is compounded annually and if you need to calculate something it’s compounded more than once per year they tell us then you need to change the compounding so by default it’s compounded annually and this example here it’s compounded annually as well because they didn’t tell us

That the interest rate is compounded anything other than annually they tell us that then we’ll have to take into account and you’ll see in the examples to follow so the first thing that we do is to put the time period it’s five years so we press five and then we press n because it’s compounded annually if it was compounded more than annually then we would have

To take that into account as well when we put in our compounding periods and then we put in the present value which is ten thousand grand so i press ten thousand and then i put it as a negative so i press plus slash minor so now am i putting it as a negative well firstly if i’m paying out this money to invest the money then it’s coming out of my business so i’m

Putting it as a negative but the main reason is that our present value and our future value must always have opposite signs if they don’t then it will be an error and the calculator will indicate that so make sure that you put your present value and your future value with opposite signs if you put one as a positive the other one has to be a negative so we put

The ten thousand right and put it as a negative and you press pv and then we move on to the next one fourteen thousand five hundred that’s the future value because it will result in the 14 500 so i press 14 500 and i press fv and all i need to do is to compute for the interest rate because i put in everything that we were given here so i press here it’s written

Cpt and that stands for compute and then i press i slash y and it has given us our percentage it’s seven point seven one percent so if i were to invest ten thousand rent today and get fourteen thousand five hundred and five years time the interest rate will need to be seven point seven one percent let’s move on to the second one if joe wants to have thirty five

Thousand run in ten years time and is willing to invest two thousand seven hundred grand at the end of each year what does the interest rate need to be for him to achieve this goal so again let me clear my time value of money calculation i press second function and then i press fv you can see on top it’s releasing clear time value of money okay now i’ve done that

Now i can start with my calculation what is it for it’s for 10 years that’s the compounding period so i put 10 again this is compounded annually because we’re not told that it’s anything other than annually and then i press n and then the second thing i put there is if joe wants to have the 5 000 right in 10 years time so this 35 000 rent is my future value but

Is willing to invest 2 700 at the end of each year so if he’s willing to invest 2 700 that is my payment or pmt so i put 2 700 and i put it as a negative because you’ll be paying this money out to invest it and then i press here it’s written pmt and then the next thing that i do is that i put the 35 000 right as my future value because that’s how much he wants

To have so i put 35 000 and then i press fd i leave it as a positive because that’s the money he’s expecting to receive in 10 years time and then all i need to do is to compute my interest rate so i press here it’s written cpt and then i press i slash y and they just given me it’s going to be 5.64 so if you want to have 35 000 right in 10 years time and is

Willing to invest 2700 right at the end of each year the interest rate that he needs to earn is 5.64 let’s look at the third one we are told here that if you can borrow 20 000 run from the bank and you are required to pay back 3 000 at the end of each year for the next 10 years what is the interest rate that you are charged so if you have to pay back 30 000 run

At the end of each year for the next 10 years by borrowing 20 000 rent what is the interest rate that is challenging well let’s clear out time value of money calculation second function fv and then we have just done that let’s see it’s likely to just clear my screen so again 20 000 run let’s see if um that’s how much you borrow today that’s your present value and

You’re required to pay back 3 000 at the end of each year that is my pmt or my payment and it’s important to note whether it’s the end of the year or the beginning of the year because that will determine how you do your calculation because you’ll have to put your calculator in begin mode if the payment will occur at the beginning of the year so you pay attention

To that and you’ve done lessons specifically on that ordinary annuity for payments occurring at the end of the year like this one or annuity due for payments occurring at the beginning of this year but in this case it’s at the end of the year just like the previous example so i put in my number of years my number of years here is 10 years so i put 10 and then

I press n and then i put in my present value which is 20 000 range so i press 20 000 and i put it as pv and that is positive because if i borrow from the bank i’ll be receiving that money today but you are required to pay back 30 000 at the end of the year so we put in 3 000 rent and put it as a negative because you have to pay this money out to repay back the

Loan and then i press pmt and then all i need to do is to compute for my interest rate so i press cpt and then i press i slash one and then it has given me 8.14 that is the interest rate that you would be charged let’s look at the fourth one quickly if you deposit six thousand run into an account that will grow to twelve thousand run in four years what is the

Interest earned if it is compounded quarterly now you can see here for this example it’s compounded quarterly so we need to tell that to our calculator remember by default this calculator is compounded annually and we’ve been fined thus far in our calculation because they were all compounded annually because they didn’t indicate but here they’ve indicated it’s

Quarterly so what do we have to do we have to change the compound into quarterly so let me press second function fv to clear my time value of my calculation and then i need to change the compounding so press here it’s written second function or 2nd and then we press here it’s written i slash y and then you can see that the payments per year is one but we are

Told that it’s compounded quarterly that is the interest rate so we put four and then you press enter and that’s what the payment if you press the downward arrow this is for the interest rate compounding you can see it automatically changes it to four as well that’s what we want our c slash y must be for okay now that you’ve done that and click c c to clear our

Screen now we can do our calculation if you deposit 6 000 right into an account so 6 000 ren is our present value put it as a negative because you’ll be depositing this money and then it will grow to twelve thousand right in four years time so twelve thousand rand is what you’ll be receiving that’s the future value and you put it as a positive and the number of

Years is four so let’s start with the number of years we press 4 but you don’t press n as yet because it’s compounded more than once per year we have to press second function first and then press n and then i press n again to confirm and what has it done just taking the number of years which is four and it has multiplied it by the number of compoundings per year

Which is four as well remember if it’s compounded quarterly that’s four times per year so always remember that you press the number of years second function and then n and then n again and then we can put in our present value is the six thousand rand so press six thousand and then we put it as a negative so we press plus slash minus and then you press pv and then

The future value is the twelve thousand right so press twelve 000 leave it as a positive and then you press fv and all we need to do is to compute for the interest rate so we press cpt and then i slash y and it has given us our interest rate 17.71 percent let’s move on to the fifth one we are told here that if you can borrow 4 000 rent from the bank and you are

Required to pay back 250 at the end of each month for the next two years what is the interest rate that you are charged now again the payment will be occurring monthly so we have to put that into our calculator so let me clear my time value of money calculations second function and then fv and i’ve just done that now i need to change the compounding periods

To monthly because it’s going to be occurring monthly the payments will be made monthly so i press second function and then i press i slash y and you can see it’s compounded quarterly as we have done in the previous example so i changed it to 12 because if payments are occurring monthly that is 12 times in a year now that we have done that press enter and then

We have confirmed if you press the download error you can see the compounding for the interest is also 12 times per year and then we press this let’s see to clear our screen now we can do our it’s borrowing 4 000 from the bank so that is our present value and our pmt or payment is 250 rand because it should be occurring at the end of each month that is ordinary

Annuity as i mentioned before and the time period is two years so we press two and then we don’t press n as yet remember if it’s compounded more than once per year you have to press second function and then press n and then you press n again to confirm and what it has done it has taken the number of years which is two and it has multiplied it by the number of

Compounding scenario which is 12 and then we put in our present value which is four thousand so it plus four thousand and put that as pv because it’s the money that you’re receiving from the bank that’s why you’re leaving it as a positive and then the 250 you put it in as a negative because it’s managed to be paying at the end of each month and then you press

Pmt and all you need to do is to compute for the interest rate so we press cpt and then press i slash y and there it has given us 42.42 very high percentage but that is what is for this example here so that’s how much interest you are charged let’s look at the last one here we are told that a 12 year loan of 70 000 rent has quarterly payments of 3 33 and 33 cents

What is the interest rate if it is compounded quarterly and the second one is if it is compounded annually and the third one is if it is compounded monthly so let’s do this one here let’s clear our memory press second function and then fv to clear the time value of money memory and then press e slash c so let’s do the first one a 12 year loan of 70 000 rent has

Caught any payments of 3 33 and 33 cents so this one here is the pmt the 70 000 rent is a pv because it’s money you’ll be receiving now if the interest rate is compounded quarterly what is it going to be so let’s calculate that one day the loan is for 12 years now you can see for the first one here if the interest rate is compounded quarterly and the payments

Are occurring quarterly so our payment compounding and our interest rate compounding coincides they’re the same so that’s a good thing if they were different if your payment compounding and your interest rate compounding were different then you’d have to take it into account so let’s do the first one the quarterly payment is 3333 so first of all let’s check if

Our compounding is quarterly so second function i slash y you can see it’s 12 so we have to change it to four because quarterly is four per year so press four and then you press enter and if you press downward arrow you can see the interest rate compounding or the c slash y is four and if you go up again you can see the payment compounding is four and that is

Accurate because our payment compounding is quarterly and our interest rate is compounded quarterly for the first one let me press this let’s see it clear our screen now we can do a calculation it’s for 12 years so we press 12 and then we press second function and then we press n and then we press n again so it has taken the 12 years multiplied by the number of

Components per year which is four and then you put in the seventy thousand rents we’ll press seventy thousand and then we put it as the pv in positive because someone you’ll be receiving from the bank and then the quarterly payment is three thousand three hundred and thirty three rand 0.33 and put it as a negative because if you’re paying this back to the bank

And then you press pmt and then all you need to do is to compute for the interest rate so you press cpt and then i slash y and you can see that it has given us our interest rate 16.22 if it is compounded quarterly what if it’s compounded annually what will the interest rate be well with this financial calculator it’s quite simple to do that so press second function

And then you press i slash y you don’t have to redo all these things again you don’t have to put in the elements again you just have to see here that the payments per year is four times meaning it’s occurring quarterly and you can see here quarterly payment so are finding that one but then you press the download arrow and then you press one because the interest

Rate will be compounded annually and then you press enter that’s all you need to do and then you press c c to clear your screen and then just press cpt and then you press i slash y and you can see that the interest rate if it’s compounded annually it will be 17.24 percent what if it’s compounded monthly well it’s just as simple press e slash c you press here with

Certain second function and then you press i slash y and the payment still occurs quarterly but the interest rate is compounded monthly so you press the downward arrow for the interest rate c slash y and then you put it as 12 because it’s compounded monthly and then you press enter that’s all you need to do and then you press c c to clear your screen and then you

Press cpt and then you press i slash y and there is your interest rate if it’s compounded monthly 16.01 i hope it has made sense i hope it was simple enough it is that simple with this financial calculator if you’re a bit confused we’d like to learn more about this one here we’ve done a lesson specifically on nominal interest rate that’s if the interest rate is

Compounded more than once per year and effective interest rate where you get the annual percentage rate you’ll find the link to that lesson in the description below you have gained value from this lesson we have learned something please subscribe to our channel like this video share it to those you think it might help and if you’d like one-on-one sessions with

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Transcribed from video

Calculating Interest Rates | BA II PLUS Texas Instrument Financial Calculator By Counttuts