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Point) A couple has decided to purchase S90000 house using down payment of $15000. They ' can amortize the balance

Question:

point) A couple has decided to purchase S90000 house using down payment of $15000. They ' can amortize the balance at 6% over 25 years_ a) What is their monthly payment? Answer b) What is the totab interest paid? Answer What is the equity after years? Answer d) What is the equity after 20 years? Answer Note: YoU can earn partial credit on this problem:


Answers

House Payments Ian Desrosiers buys a house for $\$ 285,000$ . He pays $\$ 60,000$ down and takes out a mortgage at 6.5$\%$ on the balance. Find his monthly payment and the total amount of interest he will pay if the length of the mortgage is
a. 15 years;
b. 20 years;
c.

25 years.
d. Refer to the text and Figure $13 .$ When will half the 20 -year loan in part b be paid off?

.

Party on this problem. Ah, we're given that this family has bought a turned 25,000 our house, and they paid $50,000 down trains. The president, by of the loan, starts at 175,000 And to figure out the monthly payments we're gonna do our is equal to that value divided by one minus one plus our interest rate. Ah, And in this particular one, it's a 30 year mortgage. So 30 times 12 is B negative.

3 60 uh, divided by our high volume. Can our I value for part a low kind of do it off to the side? Um, well, that A equals. I don't want to be confusing. So for her a, um, our eyes gonna be 6% interest and divided by 12 0 point 005 It would be our I value for this equation. Okay, so let's go.

Put this in our calculator. 775,000. What about one minus one plus are 6% about about 12. That's a 120.5 to the negative. 360 power, all divided by 0.6 Does that about sum so their monthly payment for the the first mortgage example is 1000 49 and 21 cents.

Okay, so they're total payment. That's their monthly payments. Their total payment. We're gonna multiply about 3 60 because they have 360 monthly payments, and that's of their total payment is gonna be 377,000 $715.60. Okay, which, if we subtract off the present by of the loan, that means the interest that they're paying is 202,000 $715.60.

It's attracted that 1 75,000 from the 3 77,000 number. Okay, for part B? Yes, apart bead. The only thing that changes is our interest rate eso it's to our interest rate off to the side. So I for this one is just gonna be, I think for part B, they wanted us to do it 6.5% so it's gonna be 0.65 divided by 12. So I have to do is go back to our last entry for part A and change those I values too.

Um, 0.65 divided by 12 Someone go do that on my monthly payment comes out to be, uh, $1106 and 12 cents. Again, we're gonna multiply about 3 60 to see the total contributions to pay this loan off. So they're gonna be paying 398,000 $203.20 Which means the interest that they're paying on the loan would be the difference between that and the 175,000. So there's gonna be 223,000 $203.20. And again, it has found that bust attracting that 1 75 from that 3 98 Okay, apart.

See, um, again, we're gonna have a new high value to think this time. They wanted 7% 0.7 Divide, about 12 is gonna be our value, and so are our value. Just change. Going back to that last entry in our calculator and changing it from 0.652 point 07 Okay, that means the monthly payment is gonna be 11 64 and 28 cents again multiplied by 3 60 Just kind of following the same algorithm. So over the course of 30 years, they're gonna pay 419,140 and 80 cents.

Yes, if we subtract 1 75 from that, we're gonna get to 44. 44,140 80 cents. Okay, that's a B and C K Part D asked for When will have the loan be paid off? So to do part D. Um, we need Teoh. Well, first off, you need to consider I'm not sure what half the loan it's referring to.

If it's referring to the 1 75 of the to 25 I'm gonna do it as if it's the 1 75 So we're gonna graph this, so rest that why want equal to 1 75 135,000 Divided about Teoh. We're gonna set our wine to value equal to our our value from Part C, which is 11. 64 28 just to figure out we can write an equation to calculate how much has been paid on. So it's gonna be one minus one plus that I value from part see with the right 10.0 7/12 here. And that's gonna be to the negative.

3 60 to about minus X all over 0.7 About about 12. Okay. And they're gonna find the intersection. And that's gonna give us our X value or the number of years or the number of monthly payments that it's gonna take Case. Let's go graph that.

That's what we're doing. 125,000 about about two. The next thing we have is Thea 11 64. 28. We have one minus the one plus 10.7 for clothes, and it's to the negative.

360 nine. It's X. It's all about about 0.7 about it. About 12. We need to change our window.

I'm probably make my X axis go up to 3 60 It's because it's to finish. It would be 360 payments. Why value? Just make sure it contains up to 1 75 sets. Have it go to 200,000. Um, and I could speak about started zero.

Uh, this should capture a good window for getting your intersection. So they're Section X is happening at 260.8 is when half will be paid off. Half of the actual alone. Uh, so that's gonna be like between the 260th and 160 1st payment will cross the halfway point, so it's gonna be the 261st payment. That is the halfway point.

Um, and we can divide to 61 by 12. So it's gonna be 21 years and nine months, and they'll be halfway done with it alone. Okay, Thank you very much..

It's needed to a more ties that alone eso the house was 310. So we got our present value of the loan is 310,000. Our interest rate, uh, is a yearly interest rates. So when you divided about 12 to calculate monthly payments, yes, we're gonna do 5.96% divided about 12. Okay, so, unfortunately, it's not.

It's not a nice decimal, so we'll have to, um, just leave it like that. It's putting our calculator just like that. Our number of, uh, periods that were paying on this is gonna be 12 months per year for 25 years. 12 times 25 300. We have 300 payments.

Okay, so our value our monthly payment, it's gonna be our present value. 310,000 divided by parentheses, one minus one plus R. I value It's gonna put that in parentheses because we've got to use that were decimal to the negative 3/100 power. All divided by r I value. Yes.

When we go put this in the calculator. So we have 310,000 divided by one money's parentheses. One plus. Hey, uh, 0.596 I've got about 12. And the meat to the 3/100 power in our denominator will also have to be that 0.596 for the red slow participant in the calculator.

Our monthly payment are is gonna be $1989 and 76 cents. Okay, uh, we're gonna multiply that about 300 to get our total contributions to pay off this loan. So in the 300 times 1989 0.76 the total we paid was 590 6000 928 and that came out. Even so, it's the total we paid. We're gonna subtract the the original present value of the loan, which was 310,000.

That's our interest. Payment was to 86 $286,928. Okay. Thank you. Very.

Okay, Number twenty or couple wants to have forty thousand five years for a Tom payment on the new house. How much is the deposit to that? A six point four person compounded quarterly It how to record amount in five years. So six point full person quarterly. We want to calculate the effective rate she does want. Plus far.

Do I buy? We have full quarters in a year. This is their point there. Six full, minus one was chemicals for So this guy is? Yeah. One us terribly ungenerous licks by fools to the force zero point zero six five five tier by tier Search five, five, five, five Hey, so after us onto infact you write each year you got five years. Let's assume you put a maybe X donors in the beginning.

One plus zero point zero six five five five to the fifth equals forty thousand. That's how much you want X equals, um, forty years found you wanted, bhai. One point zero six life. Five to the freaks. You fool.

Mother twenty five thousand one hundred. That report life and pardon me eats how much interest will be earned. So how much interest is just he used for resulting sometimes. How much department gods? The difference is the interest you earned during those for five years. Thousands of drugs you earned while eight eight.

There. Therefore time in interest. Cassie, you say can't deposit only twenty thousand. Now, how much more words I need to complete two forty thousand after five years. So if you deposit twenty thousand, only twenty thousand.

How much you earned in five years? Just put them in this form in twenty thousand would give you that many five years and you go use forty thousand to subtract this part. That's how many you need to, um, pay in five years. Time to complete forty thousand one one zero six Life forms on the books. Two seven four seven, two point five six and he's forty thousand. Just uncovered.

For profit forty two. Fear how to pay twelve thousand five. Twenty seven point four four. It is as part of C party. Suppose it can deposit twenty thousand dollar account that pace interest continuously.

What in France, right? Would they need toe accumulate the entire forty thousand five years? So that's assumes interest rate is cape. So we have forty thousand five years originally will help twenty thousand. We might have lied to the K Team five and they just solve this equation for K. I do. I buy that to take a natural lock.

Five. K equals natural of two k goes national two Divided by five Let's look off to you in about five. He's Hey ghost tear a point one three eight six So sixteen point eight six percent..

I guess this problem wants us to determine the monthly house payments are, uh, for a present value. Alone for a house is 100 99,000. Our interest rate is 7.1%. But we're gonna do this monthly, so we have to do it. That about 12.

And it's gonna be for 25 years. Its monthly said multiple 25 by 12. And it is gonna be 300 payments can. Surveys are formula for him. Amortization.

And so we have our equals. 199,000. Divided by parentheses, one minus one plus R value to the negative end power. So native 300 all over that I about a year. Can somebody get for this in the calculator of 199,000 Divided by one minus a one plus our interest rate value, which is 10.0 701 About about 12.

We're going to raise that to the negative 300 power. It's all gonna be divided by that 0.70 wind. But I've been 12. Okay, So are our value payments are monthly. Payments on this mortgage are gonna be for $1407 and 76 cents.

Is it paying that over 12 25 years? Um, at each month, we're gonna pay a total of 14. 07 176 times, 300. We're gonna pay a total in this house of $422,000 at 4 22 3 28 So that comes out to be a total that we paid. Uh, the original house costs only $199,000. Eso the amount of interest we paid was the difference.

So our contributions were over $400,000. Our interests better pay on this long. His $223,000 turn $23,328. So the interest was actually worth more than the house. Okay.

Thank you. Very.

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