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Mortgages You take out 30-year mortgage for 595 Luuu at 9.7590 be paid off monthly: If you sell your house after 15 ycars, how much will you still owe on the m...

Question

Mortgages You take out 30-year mortgage for 595 Luuu at 9.7590 be paid off monthly: If you sell your house after 15 ycars, how much will you still owe on the mortgage? HINT [See Example 7]English (United States) HEna @NTTTETTCO ACTL UTEGO 7079 igiloaniloan php ?loan-95.000 mortgage paymnents Hov auch each paymont goes payon the Ioan M d025 towrarde interesi? Amorization S6 dula taole 95 000 30 Year Toan at 5 montn

Mortgages You take out 30-year mortgage for 595 Luuu at 9.7590 be paid off monthly: If you sell your house after 15 ycars, how much will you still owe on the mortgage? HINT [See Example 7] English (United States) HEna @NTTTETTCO ACTL UTEGO 7079 igiloaniloan php ?loan-95.000 mortgage paymnents Hov auch each paymont goes payon the Ioan M d025 towrarde interesi? Amorization S6 dula taole 95 000 30 Year Toan at 5 montn



Answers

Mortgage What is the monthly payment on a 15 -year mortgage of $\$ 200,000$ at 6$\%$ interest? What is the total amount paid on this loan over the 15 -year period?

The question here asks us what the monthly payment would be on a 30 year mortgage of $80,000. So, of course, this could be taken by using equation p, multiplied by our one plus art part and over one plus R. One plus are rather let me write that one plus ours apart and minus one where P is the amount that you have borrowed. So in this particular case, would be 80,000. Are is the interest rate, which is 0.9 Divide by 12 as we're looking at it in terms of monthly payments. And, of course, if it's 30 years, our values and would be 360. So if it had to be repaid over this at this particular, um, time frame, it would give us the valley if you plug it into our calculator of $643.69 sentence. If we were going to pay it over a 15 year period, we had basically just change the value of end here. And that's just 15 times 12 which is of course, equal to 180. So which is equal to a 1 80 So if you substituted in, you would basically get the number 800 $811.41. Rewrite that, like such, and I should be your answer here.

In this problem we have the principle be related to amount the raid and the time as. Mhm. Being functional. He are empty. This is equal to he are. Do you want it by well one minus one plus r by 12. Our -12 entity Margaret kills. So this is the principal. Let's look at part of the problem. We need the monthly payment be for he has 300,000 times 30 and Raiders for person. So let's substitute. It's called the T. one. This is Marie to score percent which means there's zero point 04 He wrote it by 20 one minus one plus 0.04 x 12 minus dwell into this comes us the numerator becomes 12,000 Divided by just 12 into one minus point 302 That is equal to 12,000 to run it by 8.376. Which is equal to 1432 point $66. Let's calculate at 6%. This is born 06. derided by 12. 1 minus one plus zero. Born 0 six. might well Power -12 into I think substitute this becomes 18,000 divided by 12 into 1 -1 0.1 66 This becomes 18,000, divided by 10.008. Which comes us 179, $56. Let's look at part beyond the problem. It's called the Summers B three. Substituting the value. This is 300,000. multiplied by Greatest 6% divided by well one minus one plus Hero born 06 might well power Minour dwell into the time, which is 20 years. This comes as 18,000 divided by Dwell into one point 302 comes us 18,000 divided by eight point 376 comes us 21 48 point 99 dollars. That's

So for this for this problem, we can use the equation P p V is equal to is equal to our recurring payment times Times one minus one plus R R interest rate, which is 10.12 Or we could just say Let's leave this as interest rates right now are over 12. Since we're making monthly payments times 12 to the power of negative T. So negative 12 t and then we're gonna divide this by by our over 12 again. And so we know that our present value is 86,000 right? And so we want to know this value. We want to know what time is if we know that we were going to be paying recurring payments of 10 50. So we have we have 10 50 and then we have we have one minus one plus are over 12 and so are over 12. We can call this as we can say, this is 120.12 point 12 divided by 12. And then this is going to be times negative. 12 teeth, right? And so now we're going to divide this by again. 0.12 times are 0.12 divided by 12. And so let's see here. So we have we have 86,000 divided by 10. 50. This gives us the value of 81. So 81 times 81 times we have this value of 810.12 divided by 12. So this gives us the value of of 0.8190 So this is equal to 21 minus one plus 10.12 divided by 12 Judy Negative 12 t. And so if we if we add this one plus 10.1 to over 12 do the left hand side and then subtract 0.8190 from both sides, we get that one plus 10.1 to over 12 to the negative 12 t negative 12 t is going to be equal to be equal to one minus 10.8190 So this get this gives us a value of this is point 0.180 Not so we have. We have. Let's let's calculate the inside here. So we have one plus a value of 10.12 divided by 12. This gives us 1.1 And so now we have 1.1 to the to the negative. 12 teeth is equal to 0.18095 right? And so if we take the reciprocal of both sides, we get that 1.1 to the 12. T is going to be equal to one over one over 10.18 095 And so if we take the reciprocal of this or take it to the negative one power, we get that this is equal to 5.5 26 And so now let's take, let's say, log base 1.1 of 5.5 to 6 gives us the value of 12 teeth. So if we divide both sides by 12 we divide both sides by 12. We can isolate T, and all we have to do now is plug this into our calculator. So we have. Let's see her log base log based 1.1 of 5.5 to 6, and then we're going to divide this by value of 12. So this gives us this gives us 14.3 so so four of time is equal to time is equal to 14.3 32 years. Well, then we can say that this is approximately 14 years and four months, right, because this is one approximately 1/3 of the year and 1/3 of the year would be dividing 12 by three. So we have. We have 14 years and and four months. So 14 years and four months to pay off to pay off $86,000. And so let's see how much money we're saving here. Well, if we're paying 10 50 so this is this is actually Port A. So let's call this part eight and then for Part B, we have 10 54 or approximately, let's say, 14 years and four months. So this is This is again 14 times 12 plus for so 172 months. So 1 72 months. And the other option is paying 88 or 884 884 0.61 for 30 years for 30 years. And so 30 times 12 gives us 360 months. 04 360 months. So so for the first option, 10. 50 times 1 72 This gives us a value of 180,606 $100. So this is how much you'd end up paying total right? And so So if we paid 884.61 times value of 360 well, we would be paying. We would be paying $318,459. So So, if we want to find how much money we're saving, all we have to do is now subtract. So you subtract 318,000 459.6 by 180,600. So this gives us the value of saved Little say that saving this goes value of 1 37 859.6 year.

Okay, so we had a loan of one. Seventy. Hey, ninety two. And the interest rate is eight point one one percent founded monthly, and it's a thirty years. So how many months from thirty years? Ah, three. Sixty. You're sixteen months. Okay, so we have that one seventy a nineteen to the present day value. It will be OK. The monthly payment times Inspector of one plus zero point zero eight one Warren over twelve to the huh? One minus. Okay. One plus zero point zero eight one one divided by twelve to the negative. Three sixteen. All divided by zero point zero eight one one from brittle. You know, we just divided by the specter. Get that our our monthly payment is siggy. Looks like twelve. Sixty seven. Serving sentence. Okay. And now next, we want to find the, uh, the balance after five years. So the balance after five years, let's call it. Why is the monthly payment troll sixty seven for the seven, and then we multiply by this factor of wine minus Okay, one point, the interest rate, twelve. Instead of taking this to the negative three. Sixty, we want to subtract the number of months of pain, which is five for the number of years of impending, which is five. That sixty months of three sixty nine sixty. His three hundreds of this is to the negative three hundred divided by your point zero a one wand over twelve over. Okay, and what we get the unpaid balance after five years is going to be hundred and sixty two thousand six hundred twenty AIDS and nineteen consents.


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