Calculate Monthly Payments For Mortgage or Annuity Part A

Calculate Monthly Payments For Mortgage or Annuity Part A

entity modulus a mortgage of 190 thousand is required to purchase a house the mortgage will be repaid with equal monthly payments over 25 years at 8% compounded monthly what is the monthly payment what is the total interest paid over the 25 years well this is I think one of the best examples to understand annuity and mortgages and this is from a book and I just love this example and I want to share with all of you and the strategies which we are going to follow in this example it has Part C and D also which will be in the next part of the video okay will be used and can be used to solve most of the problems on this topic of entity ok so I'd like you to understand the method by which we are going I'm not really interested in calculating the values and impressing you with big numbers that's never my interest but I want you to make you to understand how to solve such problems ok that is a strategy behind all this so I'll leave most of the calculations with you I do have a calculator here but still I may use it sometimes but the idea here is to only give you the answers ok and the steps involved okay now let's read the problem once again it is always important to read your problem at least twice a mortgage or 190 thousand is required to purchase a house the mortgage will be repaid with equal monthly payments over 25 years at 8% compounded monthly so what is the monthly payment so that means the value of R in our formulas right the recurring amount the fixed amount the entity which you pay regularly that is what we are asking for here and the Part B is what is the total interest paid over the 25 years so you know actually it was 190,000 and once you know how much is a total paid then the difference will give you the interest that is what you paid over a period of 12 years right now so we can use the present value formula here Y present value because we know mod gauge of what 90,000 is required to be purchased in the house right so this is the present value correct so the formula to be used is the present value formula which has R in it so this I'm trying to explain with this because I've found the students struggle to figure out whether it is a present value formula or a future value formula right and I don't blame them for that it is kind of tricky right and we have made things more even more worse with them by always using a formula rather than deriving the formula as required right yeah and introducing the terms present value future value principal amount and amount they are so complicated at times but well here are simple rules once you see present value is given here mortgage of this much is required to purchase house so what do you need today is 190 thousand right so so it is a present value which is given to you so let's write down our present value form so the present value formula is PV equals tool and I suggest that you always write down all the formulas on one sheet of paper or related formulas correct so that you know exactly what to use where so the question then is to make choices which one to use so here as I said monthly payments that means recurring payments capital R and present value one night so those are the two critical things which help us decide which formula to use right so here is the formula which I am also copying from sheet read don't think I am so brilliant that I remember all these things no I don't I'm just like you and the formulas is like this right over I now here pv is a present value and r is the monthly regular payments right sometimes I use the word recurring but Arby's regular payments which you pay at the end of the month right and I is the interest now here and n is the compounding period correct so these are the terms which you should understand right so now let's see what is n first so n is a compounding Pierce the mortgage will be repaid with equal monthly payments over 25 years so the capital n I want to use as 25 years at 8% compounded monthly so every year 12 times you have to make this payment right so and interest is charged we are assuming it to be a simple entity the ordinary one so so interest is being charged monthly right and the payments are being made monthly at the end of the month that's kind of important right now so we say that in five years how many payments will you make so that is the value of n n is the number of periods or number of times you are making the payment right so we write n is equal to 25 times 12 because it is for a period of 25 years compounded monthly right so that gives me the value of n and if you multiply 25 times 12 you get the number of payments correct now I is the interest correct so how do you get interest now interest is 8% compounded monthly is that okay now that means I should be divided by 12 interest rate is 8% 8% means 8 over 102 in strength that is how it should not some time students will write just 8 right they will forget to divide by 100 so 8% means point zero eight which is 0.08 because eight over hundred so I'm not writing a to 100 but I'm reading point zero eight for eight percent right divided by 12 because this 8 percent will be charged in one year come but this compounded monthly so every month it'd be 1/12 of this so that is your interest correct if you want you can calculate these values using your calculator and write down your answers right but I'll leave them like this for the time being I'm really not doing the calculations right now that's what it is now in the formula you see you know all the terms you know PV the present value R is what you need to find and I is what this is and n is this value correct so so that's what it is now you have to plug in these values and find are correct now if I do so I get PV is 190 thousand so as I said I'm just plugging in the values leaving things for you 190 thousand is equal to R we don't know times one minus one minus and I is 0.08 over 12 to the power of minus so okay I know this is 300 because 12 times 4 is 100 I mean 4 times 25 is 100 and this is 300 so let me write 300 it becomes too complicated at times so this is simpler so following a simple step okay so I wrote 300 for that now I is 0.08 over 12 I definitely need a calculator I could simplify this also but let's forget about it now okay so we get all these values plugged in here and from here we can calculate the value of our correct so what will be our our will be you to multiply this with this first is it ok so let me show you that part because I've seen students making a mistake at this step also now R is equal to so you've got one 90,000 here you do 190 thousand right and then you have to multiply by this number so I'm putting it in bracket right 0.08 over 12 it is good to put it in bracket because you know once you use your calculator you can do these operations in a straight line and get exact answer if you do them separately then sometimes there may be decimals which you will be rounding and if the powers are like 300 you can imagine what mistakes you can make right and we don't want to pay more for all this correct so so my advice is write it in this form and then so we got rid of this it got multiplied with 190 thousand and to find our we have to divide by this whole thing here under this value right so what I'm doing here is I'm using the simple device it's not a good way to write but it's not a bad way because we are going to use calculator to calculate this out and I'll put all this divided by by all this because when it comes here it is to be divided by all this is it okay so now put one big bracket here and one – and this is like 1 minus 0.08 over 12 to the power of minus 300 right okay so that's what it is so if you plug in all these values in your calculator hands press equal to you should get some answer like this now let me write here the answer is fourteen sixty six point four or five something and surrounded to four or five is it okay so that is the dollar amount which is being paid regularly every month end for twenty five years to make a mortgage payment right so took any ball so that is what the answer is so so what is the monthly payment that is the total monthly payment which you make okay now monthly payments made this much how will you find so we're done Part A what is the monthly payment which is fourteen six to six point four five right we'll use Canadian dollars for the time being as nothing else is mentioned here right so that's good and I forgot to write dollars here let me write dollars here and these are all Canadian dollars okay so that's what we pay now Part B is what is the total interest paid over 25 years so think like this in 25 years how many payments did you make let me now write 300 we use the value 300 so 300 is the total number of payments we made of what amount fourteen sixty six point four five so actually we paid three hundred times fourteen sixty six point four five correct instead of 190 thousand so the difference between them actually goes towards the interest right so we see well this is our part a and the Part B is interest right so let's figure out what the interest is so let me write down interest is equals to let me push this page a bit forward I know they're going right on the margin now so interest will be total amount paid is fourteen sixty six point four five times three hundred because this is the number of installments right this is monthly installments of three three hundred installments of 1466 point four five so we'll say fourteen sixty six point four or five times 300 is the actual payment we made over a period of 25 years for the mortgage of 190 thousand so instead of paying present value of what ninety thousand eunsuh now we paid that much and that difference gives you the interest correct and you'll be shocked when you see this figure okay so the answer is before me and it says the interest is to forty nine is not to forty nine this to forty nine thousand nine thirty five so that is the interest paid and that's the answer for Part B so remember one thing in mortgages you normally pay much much higher than what you really have to pay currently of course when you don't have money you have to borrow and pay for it correct now so the Part C which I am leaving for you is find out what percent of total amount paid is interest so you pay it you know one forty six point four five times three hundred that much amount and this amount is what percent of one ninety thousand right so figure that out is a huge huge amount right so you can see from here that the house costing less it two hundred thousand is making you pay two hundred and fifty thousand extra on it so it is almost four hundred fifty thousand you understand roughly speaking so two hundred plus 250 right so double the amount more than that is being paid as an interest or twenty five years okay now in the next video I will talk about the normally in the market when you go for a mortgage they may tell you to renew it after five years right and they may not give you the same rate which you get now so we will look into the scenario what happens if you first take a mortgage for five years and then our market is raining for rest of the time okay and how does it impact our payments correct so that will be my next video on this so have a good look at it try to understand do your calculations and hopefully the way I have laid it out helps you to understand and calculate with your beautiful calculator thank you

Actuarial science

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