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In order to purchase a truck Shandex Transport (ST) obtained a $50,000 loan for 5 years at 7.8% compounded semi-annually: The loan is structured to reduce the balan...

Question

In order to purchase a truck Shandex Transport (ST) obtained a $50,000 loan for 5 years at 7.8% compounded semi-annually: The loan is structured to reduce the balance owing to 510,000 at the end of the 5 year period. How much are ST's payments at the end of each month?Select one:a, S804.87b. $868.84cS1143.3454206.04

In order to purchase a truck Shandex Transport (ST) obtained a $50,000 loan for 5 years at 7.8% compounded semi-annually: The loan is structured to reduce the balance owing to 510,000 at the end of the 5 year period. How much are ST's payments at the end of each month? Select one: a, S804.87 b. $868.84 cS1143.34 54206.04



Answers

Al needs to borrow $\$ 15,000$ to buy a car. He can borrow the money at $6.7 \%$ simple interest for 5 yr or he can borrow at $6.4 \%$ interest compounded continuously for 5 yr. a. How much total interest would Al pay at $6.7 \%$ simple interest? b. How much total interest would Al pay at $6.4 \%$ interest compounded continuously? c. Which option results in less total interest?

Amortization table. But to do that, we have to first calculate our our value eso that the present value of this loan is $110,000. Uh, in order to find that hard, but you have to divide that by one minus one. Plus our interest rate. This is a semi annual payment. Eso then the interest rate is 8%. So that means we're ready one minus 1.4 It's gonna have a nine payments system E to the negative. Ninth power all over 0.4 Okay, So hadn't or calculator. So we have 110,000 and one minus 1.4 to the ninth. Power called about about 0.4 So each payment is gonna be for 14,794 dollars in 23 cents. Okay, So the next step to creating our amortization table, um, we're going Teoh, Just send it up. Probing. He only wants the 1st 4 so we just do 1234 Ah, the amount paid is that 14,000 number. So it's always gonna be that 7 14 1007 94 780 but it's just that number from above and 23 cents. Our interest value that were gonna pay on the loan gets calculated each time. The portion that goes towards paying off the principal will get by subtracting the interest that gets calculated from the actual amount paid. We have a capital principle that needs to get paid off. So our first, uh, thing we do is we set it up at our zero level. Okay, then we have an amount that we're paying first. Okay, so if we pay Ah, wait. Any calculator interest? So that interest on 110,000 for first payment, we're gonna pull 4400. Now, I was subtracted off of our payment, really? Making a payment of 10,300 $94 and 23 cents, which is gonna leave as our principal of 99,000 $35 and 77 cents. Okay. Again, we're gonna take 4% of that. So we're gonna have 39 84 23. We're gonna take that off the top of our our initial payment. It's got to get our portion. It goes towards the principles. 10,810 initially is our principals sitting at 88,000 $795.77. Okay, finding 4% of that. We have 3500 $51 in 83 cents. If we subtract that from the actual payment, we're actually paying off $11,242 and 40 cents off of our principal, which leaves us with $77,553 and 37 cents. And then the last one I'm recording here multiply that by 4% and we have $3102 and 13 cents. Which leaves us with 11,600 $92.10 going towards the principle, which puts the principal at 65,000 100 $61 in 27 cents. We just keep going and following that algorithm until the loan gets paid off, they should be after the ninth payment. Thank you very much.

Wants me to find, um, the monthly payment alone. So the loan was 4 $14,000 Um, so in order to find our value gonna divide our present value but one minus one plus our interest rate. So our interest rate is gonna be one plus 0.7 to about about 12. Its monthly for four years. That's gonna be to the negative. 48th power, divided by 0.7 About about 12. Okay, so we're just gonna go put that in our calculator? So we have 14,000 I divided by one. This is the one plus 0.7 About about 12. Native 48 power and then divided again by 0.7 About about 12. So his monthly payments are going to be $335 and 25 cents. Okay, as parting in part B is the total amount of interest, so he's gonna pay that for 48 months. Okay, so the total amount that he pays, it's $16,092. And so because the president was 14,000 them is the amount of interest that he pays is gonna be $2092. Thank you very much.

Okay, So for part A, we're looking for our periodic payment value. We're given the present value of the loan as $5500 were given that the interest rate is 10% but it's compounded monthly. Eso is gonna be, uh, the ivory. We're gonna use a zero points here. Uh, 0.10 Where is your just 0.1 divided by 12. And our number of periods? It's gonna be for 24 months. Okay, so we can calculate this by using a formula. So our values eagle to our present value, divided by one minus one plus are interest rates. So one plus point 1/12 into the negative. 24th power. I'll divided by playing 1/12. Could just be careful with all your units in the calculator. Okay, I'm gonna get put down to talk to her now, so we have 5500. Okay, So we're gonna do in parentheses one minus one. Plus, I'm just gonna keep all this in the calculator to so it keeps all of our around the errors to a minimum plus point 1/12 to the negative 24th power. All that but it by plant wine every and so our monthly payment is going to have to be $253.80. Okay, so there's parting. It's a for B. Pretty again, Part B. We have $253.80. Multiply that about 24 to see how many total payments we've made. The grand total. We've paid out $6091 and 20 cents King and then are the president's A lot was 5500 which means that our interest, according to the formula, is going to be 500 $91.20. Okay, so Part C wants with me to make an amortization table. So, like I've been doing before, I'm just gonna give you the first row and then, uh, go over to excel and use that to calculate the rest. So we have X, which is just what payment number it ISS We haven't I which is the interest based on our previous principle. So our first principles going 5500. So our first payment claiming to 53 80 our interest on that loan to 5500 he's gonna be $45.83. Okay. And then the portion of the amount paid, it's gonna be 207.97 That goes towards the principal. And then we take that off the principle to get the last column. So our new principles $5292 and three cents. Okay, so we do the rest of excel because we have to go for 24 months. So we're gonna need some sort of spreadsheet to manage this. So are 24th column. It will have the same amount paid. We're gonna have a different interest portion and principle. So we calculate that and I'll be back. Okay. After that pause, I'm now back. Um, my spreadsheet told us that her final amount coming up off of interest is gonna be $2.10 which means the portion of the amount paid that goes towards the principle is gonna be $251.70. And then our principal, after all this sudden done, will be at negative 0.7 cents, which means we get seven cents back on that last payment. So going back, We can, uh, get seven cents back. So the total that we ended up paying was 6000 $91.13. Okay, we're gonna take off the 5500. That was the president value. And so the amount paid by interest was $591 and 13 cents according to the amortization table. Thank you very much.

Okay let's look this big massive equation we have here um Where p. Is the monthly loan payment? A represents the loan amount. Rs. C. N. Annual interest rate as a decimal will be given as a present converted to decimal when using in the formula and he represents years. So apparently if we know the loan amount, the interest rate and the number of years or the term for the loan then we can calculate the monthly loan payment using this formula. How did they get this formula? I don't know but we don't really need to know how they got the formula. We just need some numbers to plug in. So suppose that the loan amount is $20,000. $20,000. An annual interest rate is 4%. So that is my value of our um that is equal to four hundreds which is 40.40 point 04 And the number of years say the term for this is five years then to calculate the monthly payment, all I need to do is plug in these numbers into the formula that were given. So to find the monthly payment. Given these conditions use the formula the payment would be I mean you can't tell just by looking you have to take 20,000 times. Are I need to make sure I use that decimal form. Not for because that's the percent. That would be 0.0 4/12. Or divided by 12. That's the numerator. All that's going to be divided by one minus one plus crs. Again we have ours 0.4 divided by 12 raises the power of negative 12 times. T. You put that in parentheses to put a five because finally get to use T. So this crazy expression numerator, we have the loan amount times the rate divided by 12 denominator. We have one minus this quantity one plus the rate divided by 12. That quantity has raised the power of negative 12 times. T. Looks all pretty crazy. Um And so what this is equal to make it green for money. If we round it to the hundreds we get a number that looks like something I did in the calculator already. Yeah 300 $68. And yeah we're under the 100 for money. So if you ever taken out alone there's some really crazy formulas going on behind the scene um To calculate your monthly payment. Now the way that I did this was in multiple ways I first mitt 84 calculator where I evaluated the numerator and get track of that number, evaluated the denominator very carefully and keep track of that number. And then I took the top numerator divided by the bottom the denominator. And then I rounded now. What I would encourage you to do if you don't already use it um is to try dez most dot com slash scientific scientific calculator. Because you can see as crazy as this expression is India's most. You can type it in just as I have it written down here. You can type really complicated expressions into DEz most and it calculates it $368.33 and all that extra stuff at the end there. Um This is essentially just a plug and chug problem. Order of operations. Simplify the numerator and then simplified the denominator and then divide top divided by bottom to get your answer. Um You know we could probably write this out in a bunch of steps, step by step going, breaking it down. But we have technology to help us out. Monthly payment is $368.33. Thank you for watching


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