Create a Car Purchase Receipt for R&D Effortlessly

Car purchase receipt for R&D

in this video we're going to talk about how to calculate the monthly car payment of a car loan so let's work on this problem here sally takes a 10-year 30 000 loan to purchase a car at a six percent fixed annual interest rate what is sally's monthly card payment feel free to pause the video if you want to try this problem so the formula that we're going to use is this equation the monthly car payment is going to be the principal times the fixed annual interest rate divided by n now n is the number of payments that will be made in one year since we're trying to calculate the monthly payment and there's 12 months in a year n has to be 12. so we're going to divide all of this by 1 minus 1 plus r over n raised to the negative nt so that's the formula that you need in order to calculate the monthly payment of any loan so let's write down what we know we know the principle of the loan it's thirty thousand dollars now sally didn't put any money down so this is just the beginning balance of the loan the annual interest rate is six percent now we need to convert six percent to a decimal in order to do that divide by a hundred six percent divided by a hundred is point 0.06 so that's what we need to plug in for our r value now the next thing that we need is n and t we know that n is 12. now what is t t is basically the term of the loan it's the time in years and since this is a 10 year loan t is going to be 10 years now let's go ahead and plug everything that we have into this formula so we have the principal which is 30 000 times r over n r is 0.06 and is 12. all divided by 1 minus 1 plus r so r is the same 0.06 n is 12 raised to the negative n and then times t t is 10. so let's do this one step at a time 30 000 times 0.06 divided by 12 that's 150 this is going to be divided by 1 minus 1 plus 0.06 divided by 12 is 1.005 negative 12 times 10 that's negative 120. so go ahead and plug in this entire thing in your calculator make sure to put two sets of parenthesis and don't forget to close it at the end otherwise your answer might be different so the final answer is 333 dollars and six cents so that will be sally's monthly car payment given this 10-year 30k loan now what we have here is an online calculator if you go to google and type in online loan calculator this website should post up bankrate.com and it's a nice you know way to calculate your monthly payment for any loan so we can confirm if our answer is correct in our example we had a 30 000 loan the loan term was 10 years or 120 months and we had a fixed annual interest rate of 6 percent and this is the exact answer that we got the monthly payments is three hundred thirty three dollars and six cents the total interest paid on this loan is nine thousand nine hundred and sixty seven dollars and thirty eight cents you can also check out the amortization schedule if you click this so you can see starting from september 2022 after you make your first payment some of it will go to the principal some will go to the interest and this will be a balance so this will eventually be paid off 10 years later august 2032 so i do have another video that explains how to create an amortization schedule and how to do so using excel so if you go to youtube and type in amortization schedule organic chemistry tutor that video is going to come up for those of you who might be interested in that now let's work on another example it's very similar but slightly different megan takes out a 20-year term 90 000 loan to purchase an electric vehicle at a five percent fixed annual interest rate now she makes a down payment of 10 000 towards the purchase of this car what is megan's monthly car payment so let's begin by writing the formula the monthly payment is going to be the principal or the balance of the loan times the annual interest rate divided by n and this is all going to be divided by 1 minus 1 plus r over n raised to the negative nt so let's write down what we know what's the value of p in this problem p is the principal now she took a 90 000 loan but she made a down payment of 10 000. so when the process begins the balance of her her loan is going to be eighty thousand it's ninety thousand minus ten thousand so she's going to start with a principal balance of eighty thousand r the annual interest rate is five percent now we need to convert this value to a decimal so 5 divided by 100 is .05 since we're still trying to calculate a monthly payment and not a quarterly payment or a weekly payment and it's going to remain 12. now this is a 20-year term instead of a 10-year term loan so t is 20 years now let's go ahead and plug in everything into this formula so we're going to have 80 000 times r r is 0.05 divided by 12 all divided by 1 times 1 plus r over n raised to the negative and t so n is 12 t is 20. so let's simplify this 80 000 times 0.05 divided by 12. this is 333.3 repeating one plus .05 divided by 12 that's going to be 1.00416 repeating now 12 times 20 is 240 so this is going to be raised to the negative 240. now let's go ahead and plug everything in so 333 now for to write point three repeat and just type in three thirty three point three three three three three add a few threes in there to make sure you get a fairly accurate answer and then when you plug in 1.00416 add a few sixes in there too maybe like three or four that'll keep the final answer accurate to the nearest hundredth place which is what we need to round it to so the monthly payment that i got is 527.96 so that's how much megan is going to have to pay each month for 20 years in order to pay back this particular loan now let's make sure our answer is correct so let's plug in the loan amount which is ninety thousand minus ten thousand so we're starting with the eighty thousand dollar balance the loan term is for twenty years and the interest rate was five percent calculate and this is the answer we got 527.96 the total interest that must be paid on this loan is pretty high forty six thousand dollars so this is something that you wanna reduce the best ways to reduce the total interest paid is number one try to get a very low interest rate number two you wanna keep the amount that you the loan amount keep it as minimal as possible so try not to spend more than what you can afford or overdo it number three is the loan term if you can decrease the term of the loan this is going to increase your monthly payment so you're going to pay it off faster but it will also reduce the total interest paid because interest has less time to accumulate so those are some ways in which you can reduce the total interest paid on any loan reduce the the loan amount that you're taking try to pay it off faster or reduce the interest rate on which the loan is based on