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4.0.27Soroono noods to borrow $13,000 Io buy and Iho porson has dotarmlnod Ihat monthly payments of 5275 are allordablo. Th al 8%0 APR; 4-year Ioan at e 5%0 , Or 5-...

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4.0.27Soroono noods to borrow $13,000 Io buy and Iho porson has dotarmlnod Ihat monthly payments of 5275 are allordablo. Th al 8%0 APR; 4-year Ioan at e 5%0 , Or 5-year loan al 9%0 APR: Which loan bosl moels Ihe person s neods? ExplainThe lhird loan bost moets the parson'& needs bocause Ihe monthly paymant of 5 month The first Ioan best meets the person s needs because the monthly payment ol $ month: None of Ihe loans moet the person'$ needs:Ioss Ihan the maximum budgeled aless tha

4.0.27 Soroono noods to borrow $13,000 Io buy and Iho porson has dotarmlnod Ihat monthly payments of 5275 are allordablo. Th al 8%0 APR; 4-year Ioan at e 5%0 , Or 5-year loan al 9%0 APR: Which loan bosl moels Ihe person s neods? Explain The lhird loan bost moets the parson'& needs bocause Ihe monthly paymant of 5 month The first Ioan best meets the person s needs because the monthly payment ol $ month: None of Ihe loans moet the person'$ needs: Ioss Ihan the maximum budgeled a less than tha maximum budgaled a



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You want to buy a car, and a local bank will lend you $\$ 20,000$. The loan would be fully amortized over 5 years $(60$ months), and the nominal interest rate would be $12 \%,$ with interest paid monthly. What is the monthly loan payment? What is the loan's EFF%?

All right, everybody here on this problem. We've got another loan problem now. It's not quite as complicated as it looks. Right. So let's try and run through this. They're giving you two options here. Okay? Option number one is 0% interest. 48 months, and then the car costs $18,000. Option to still 48 months, 7.98% interest. Now, the car still cost $18,000 but they give you a $2000 discount if you take this option. So it means the car is really only gonna cost $16,000 over here. Now, you want to use this formula that they give you to determine which of these two options is gonna be the cheapest for you? All right. Now, let's just think about option number one over here for a second. Hey, forget the other parts. That's just looking. Option number one. Now it's 0% interest. So it means your monthly payment. Your monthly payment is just going to be how much it costs you. Total divided by how many total payments you have. 18,000 divided by 48. You don't need you to use that complicated formula for this part because there's no actual interest involved. It's just how much the car costs, divided by how many different payments you're going to make on it. That's when you do that. That uses 375 so the monthly payment for that option is gonna be $375. So now it's consider option number two here, Instrumental up here. Let's look at option number two because option number two has actual interest involved. A 7.98% interest that tells you you're gonna have to use that formula here. So it tells you it's 48 months in is the number of months you have. That means in is equal to 48. So in this formula, everywhere that there's an end, let's come back up here and replace both of those ends with a 48. The Metro Pier replace both of those ends with a 48. It's 7.98% interest that tells you what your art is. So are is 0.798 a 0.798 You have to have your interest as a decimal, and so that's what we need to come back up here and replace all of our ours with I see no 0.798 0.798 went 079 It's all of our ours. It replaced with that 0.798 because that's what her interest is. And that's what our represents. And then the car cost $16,000 because you got that discount. And so that's our A values. We need to come back up here, replace that, eh? With 16 1000. So here in the formula, we have replaced all those variables with numbers. So now we're just gonna type this in on a calculator. I'm doing a type in the top first and then the bottom separate and then divide them. All right, So let's just look at the new marine retreat. Put princes where they haven't switched to 16,000 times princes 0.798 Divided by 12 closer princes. Times open. Another 11 plus 0.798 divided by 12 Close that princes raze it to the 48th power. And so I think that should give us 1 46 point 255 And so that's what that top went to. And then here on the bottom of two princes, one plus 10.798 divided by 12. Close the princes, raze it to the 48th power and then subtract one. And I gave me 0.37 for six. And then now let's take these and divide them. We've got 1 40 search 400.255 divided by 0.3746 and that's 390 0.43 a $390.43. So that's how much your monthly payment would be on option number two. It's option number two would be 3 90 0.43 So which of the two options is cheaper? Option one's $375 a month Option two is $390.43 a month, and so it tells you option one is gonna be your cheaper option

The given part in this question is and auto mobile dealer offers, these two must no down payment three year loans at an interest in them. The customer can afford to pay $500 per month. We need to find the guys off the most expensive part that can be purchased. Let l dollars the price off the car here. Given this equals 23 years, R equals to 10%. Will stand by. Hundreds will be your appointment. Monthly payment things, um equals two $500 and gays one plus are by 20 the whole power 20. Now we will put all the values here. Value for NT equals toe one place deal point fun divided by 12 full power value of peace Is he turned into threes 36 value of case one simplifying it. We were at one point 3481 Big six. No monthly payment is m equals two. I'll multiplied by are multiplied by K divided by well multiplied by my husband people there and find the value fell. I'm equals to 500 Boston l multiplied by the your 0.1 multiplied by 1.348 point 66 divided by 12 multiplied by value of case 1.348166 minus one. You will be zero point before 81 and equals two. 500 multiplied by 12. Slide by 0.34 81 It divided by 0.1, multiplied by one point in 481 six one. Simply fangled. We will get the value of families. Looks in there. 15,495 points. Extra dollars. Yeah, Thank you.

Hi. We're here with a differential equation. Initial value question and the context is were essentially alone. Bad loan payoff. Where we're gonna find out that with the current situation, we will never be all the path alone because of the either the monthly payment amount or the initial amount of money that was borrowed. So first, I'm gonna solve this initial value question, and then we're gonna talk about why your debt will only increase, given the current situation. And then what would be the amount match amount originally borrowed in order for you to not be going further and further into debt monthly. And then there's this, um, a few additional questions toward the end. Recall that this type of differential equation okay, which looks like or comes in this form. Why? Prime of tea equals Okay, why? Plus b can be solved in general with this form, why of t equals some constant C raised to the K T minus B over K. Well, in this case, we have our be value here. We work a value here. We also have an initial condition here so I can go ahead and plug everything in salt for C so I'm gonna pull again. 40,000 equals are constant, which we don't know Times e raised to zero because you're gonna have zero times your 00.3 which is this gonna be zero minus a negative 600 over 0.3 So we go ahead and clean this up. We end up with 40,000 equals, just see, plus 20,000. In other words, C equals 20,000. And so our final answer would be, in this case, be of tea. Go back to the context of the problem equals 20,000 e raised to the 0.3 T plus 20,000. So that would be your your solution to this particular differential equation. And given the initial conditions, the question is how What amount of money, um, to start off with would ensure that we don't go further and death and the reason why we're this is a increasing function down to the question is because 0.3 of your initial okay, which is 40,000 Jews in different color point threes of 3% of 40,000 is 1200 and 1200 is more than your payoff, so you'll actually owe more each month because you will never be able to pay off the loan amount and interest. So the question is what would be an initial value that would ensure we at least don't go further into debt. And that is we want to know 0.3 of what equals 600. And if you saw this problem, well, we've already seen that you get 20,000. So we would want we would want a an initial loan value of 20,000. Turn sure that we at least don't go further into debt each month because 3% of 20,600 which would take care of that pain in general if we're given a similar situation. But we have a complete general case where a positive rate have a positive payment and we have obviously a positive month. We borrowed what we need to have Is this be true in order for this to have a net value of zero so that our rate so we're at increasing or owing more per month. So in other words, we would need to have this be evil to our initial amount borrowed in order for us to not go further into debt

Let's use this compound interest formula with a principle of $1000. That's the amount that was borrowed and an interest rate of 9% which, as a decimal, is 90.9 And let's figure out a the final amount, which would be the amount that needs to be repaid at the end of six months. So what you're going to do is type this entire expression into your calculator and then round to the nearest penny, and you get $1045.85.


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