Mortgage points, also known as discount points, are fees paid directly to the lender at closing in exchange for a reduced interest rate. The chart below shows three options for a qualified lender who wants to borrow $200,000 at a 30-year term from a local bank called First Lending. https://gmatclub.com/forum/download/file.php?mode=view&id=80024Susanne is trying to buy her first home and has only been approved by First Lending for a loan of $200,000 or below. She has $10,000 in cash on hand that she will spend on her home purchase for any of the three upfront costs (down payment, fees, and/or points) and she must keep her payment to First Lending under $1000 a month. First Lending requires that the homebuyer put down at least 20% on the purchase price of a home along with a fixed closing cost of $2500. As an incentive to move to the region, Susanne’s employer offers a special program in which the company will provide a one-time bonus payment for a down payment of 20% of the purchase price of any home in the region, with a payment limit of $60,000. This amount can only be used for the down payment and must be paid back if the employee does not remain with the company for at least 5 years. 13.jpg

Question 1: For anyone without much of a banking or mortgage background, here are a few points that initially confused me when reading this question: "Paid at closing" means the mortgage points are paid upfront when the loan is originated , not at the end of the loan term. In a mortgage, each monthly payment consists of both principal and interest . The outstanding loan balance decreases over time as principal is repaid. Interest is charged on the remaining balance , not on the original loan amount throughout the entire term. Because of this, a calculation such as 4.25% × 18,000 − 4% × 17,000 does not correctly represent the difference in the total amount paid under the 1-point and 2-point options. Mortgage interest is calculated on a declining balance over the life of the loan, so the correct approach is to compare the total monthly payments under each option (including the difference in upfront point costs).

Mortgage points, also known as discount points, are fees paid directly : Multi-Source Reasoning (MSR)

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Sure thing!

The question asks "Click Yes if the loan at that payoff date would involve less total cost than the same loan with no points purchased. Otherwise select No." In other words, we're comparing the costs of two loans after t amount of time.

One loan has two points and the other has none. So, if $Cost \ of \ 2 \ point \ loan < Cost \ of \ 0 \ point \ loan$, then we click yes. This is the same as $Cost \ of \ 2 \ point \ loan - Cost \ of \ 0 \ point \ loan < 0$.

That means if the difference is < 0, then click Yes, otherwise No.

I hope that answered your question!

iamchinu97

Bismuth83 can you explain more on Question 3. I did not get of greater than or less than 0 is giving us the intended info

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for q2, but she needs to keep her EMI below 1000$ a month which is not possible for a 204K loan as the emi with 1 point will come out to be 1003.55$.

Can someone pl comment?

Thanks

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I'm a little bit confused where you got the number 204k and which part of question 2 you're talking about.

If she can take out a 1-point loan and cover the initial cost, the EMI will be equal to $983.88. This is based of the chart in tab 1.

Let me know if I misunderstood anything!

GaganGujral

for q2, but she needs to keep her EMI below 1000$ a month which is not possible for a 204K loan as the emi with 1 point will come out to be 1003.55$.

Can someone pl comment?

Thanks

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I just re-read the question, it says a minimum of 20% down payment is required (just as in the real world), so she can always use the extra $5500 (balance) cash to pay a little more than 20% down payment and bring the loan down from 204K to sub 200k.

In that case, the loan of 255K becomes possible for her to afford!

right?

Thanks for the reply though.
Appreciate!

Gagan
Meditate & Gmat!

Bismuth83

GaganGujral

for q2, but she needs to keep her EMI below 1000$ a month which is not possible for a 204K loan as the emi with 1 point will come out to be 1003.55$.

Can someone pl comment?

Thanks

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Yeah that's exactly right. Good job!

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where is my calculations wrong for Q3 part 3

1 jan 2021 = 40 months from 1 march 2015

cost for 2 points = 40*954.83 + 4000 = 42192
cost for 0 points = 40*1013.37 = 40534.8

means cost for 2 points is greater than cost for 0 point That means cost for 2 points at this particular date is NOT LESS than cost 0 point

Bismuth83

Question 1.

1. To find the total cost difference between the two loans, we have to look at what is different between the two.

2. The 2 point loan costs $2000 more for the extra point and also costs $29.05 less for each monthly payment.

3. Now, let's put this info together with the knowledge that Susanne pays for 30 years or 360 months: Cost of 1 point loan - Cost of 2 point loan = $-\$2000 + \$29.05 * 360 = \$8458$, which is closest to the answer $8,500.

Question 2.

1. Let's consider each home and check whether it's possible for her to buy.

2. Home A: $327,500 with 1 point. The down payment is $0.2 * \$327500 = \$65500$. The 1 point and closing cost are $2000 and $2500, respectively. Together, it would be $\$65500 + \$2000 + \$2500 = \$70000$. She use the $60000 on the down payment and $10000 in cash for the remainder and other costs. The remaining sum for the house would be $0.8 * \$327500 = \$262000$. With no other methods of payment, this cost would be above the $200000 cap on the loan. So, this house doesn't work.

3. Home B: $255,000 and 1 point. The down payment would be $0.2 * \$255000 = \$51000$ and Susanne could use the bonus $60000 to cover it up. She then can use $4500 of her $10000 for the 1 point and closing cost and it leaves her with $5500. The remaining sum for the house is $0.8 * 255000 = 204000$ and Susanne can use the rest of her money to bring it below $200000, making it possible to cover all costs. So, this house is possible.

4. Home C: $259,000 and no points. The monthly payment would be $1013.37, which is more than $1000. Susanne wants to keep this number under $1000. So, this house doesn't work.

Question 3.

1. The difference between the two loan plans is the cost for points (a difference of $4000) and the monthly payment (a difference of $58.54 per month). "Yes" means that $Cost \ of \ 2 \ point \ loan - Cost \ of \ 0 \ point \ loan < 0$ and "No" if otherwise.

2. September 1, 2020. $Cost \ of \ 2 \ point \ loan - Cost \ of \ 0 \ point \ loan = \$4000 - 66 * \$58.54 = \$136.36 > 0$. No.

3. November 1, 2020. $Cost \ of \ 2 \ point \ loan - Cost \ of \ 0 \ point \ loan = \$4000 - 68 * \$58.54 = \$19.28 > 0$. No.

4. January 1, 2021. $Cost \ of \ 2 \ point \ loan - Cost \ of \ 0 \ point \ loan = \$4000 - 70 * \$58.54 = -\$97.8 < 0$. Yes.

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mkeshri185

January 1, 2021 is 70 months, not 40 months, from March 1, 2015.

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oh ****... my mistake... sorry for minor nuance.

Bunuel

January 1, 2021 is 70 months, not 40 months, from March 1, 2015.

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Question 1:
For anyone without much of a banking or mortgage background, here are a few points that initially confused me when reading this question:

"Paid at closing" means the mortgage points are paid upfront when the loan is originated, not at the end of the loan term.
In a mortgage, each monthly payment consists of both principal and interest. The outstanding loan balance decreases over time as principal is repaid.
Interest is charged on the remaining balance, not on the original loan amount throughout the entire term.

Because of this, a calculation such as 4.25% × 18,000 − 4% × 17,000 does not correctly represent the difference in the total amount paid under the 1-point and 2-point options. Mortgage interest is calculated on a declining balance over the life of the loan, so the correct approach is to compare the total monthly payments under each option (including the difference in upfront point costs).

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shouldn't the passage be " The chart below shows three options for a qualified borrower who wants to borrow $200,000 at a 30-year term from a local bank called First Lending " instead of " The chart below shows three options for a qualified lender who wants to borrow $200,000 at a 30-year term from a local bank called First Lending "

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Exactly

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I could be completely missing something obvious here. But in question 3. In the total cost of the load, why are we not including the remaining outstanding principal that has to be paid for the early closure?
I'd expect to compare: Instalments so far + Outstanding balance + Points cost + Closing cost

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Calcualation is too intensive and hence not great quality from calc point of view
for example in q3, every part should be solvable using an approx value of 60 and that doesn't work in 2nd part of it

and in Q2 part 3 , loan value could be less than 200k and hence we cannot directly conclude it using 1013 as emi

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Hi Ditipriya,

Your instinct isn't wrong. The full cost of a single loan really would be: installments paid so far + outstanding balance + points + closing cost. So your formula is a fine way to describe one loan's total cost.

The key is what Q3 actually asks: it compares the same $200,000 loan under two options (2 points vs. 0 points) at the same payoff date - and asks which one costs less. When you compare two things, anything that's identical in both cancels out and can't change the answer.

Look at what's the same in both options:

- Same borrowed amount - she took a $200,000 loan either way, so the principal she still owes at the payoff date is the same debt in both scenarios.
- Same closing cost ($2,500 from the Home Buyer Profile tab) - paid in both.

So the outstanding balance and the closing cost appear on both sides of the comparison and drop out. What's left - the only things that actually differ - are:

- The points cost: $4,000 (2 points) vs. $0.
- The monthly payment (from the Mortgage Point Chart tab): $954.83 vs. $1,013.37, a $58.54 gap each month.

That's exactly why the posted solution only weighs $4,000 against $58.54 x months. It isn't ignoring the outstanding balance - it's canceling it because it's common to both.

A tiny stand-in to feel it:

Two ways to buy the same $100 item.
- Option A: pay a $10 fee upfront, then $5/month.
- Option B: no fee, then $6/month.

Whenever you settle up, you still owe the same $100 on the item in both plans - so that $100 never decides which plan is cheaper. You only compare the $10 fee against the $1/month you save.

Same move here: strip away everything shared, and only the points-vs-savings tradeoff is left.

Answer: No, No, Yes

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Home A: $327,500 with 1 point. The down payment is
[ltr]0.2∗$327500=$655000.2∗$327500=$65500[/ltr]
. The 1 point and closing cost are $2000 and $2500, respectively. Together, it would be
[ltr]$65500+$2000+$2500=$70000$65500+$2000+$2500=$70000[/ltr]
. She use the $60000 on the down payment and $10000 in cash for the remainder and other costs. The remaining sum for the house would be
[ltr]0.8∗$327500=$2620000.8∗$327500=$262000[/ltr]
. With no other methods of payment, this cost would be above the $200000 cap on the loan. [color=#e82a1f]So, this house doesn't work.[/color]

3. Home B: $255,000 and 1 point. The down payment would be
[ltr]0.2∗$255000=$510000.2∗$255000=$51000[/ltr]
and Susanne could use the bonus $60000 to cover it up. She then can use $4500 of her $10000 for the 1 point and closing cost and it leaves her with $5500. The remaining sum for the house is
[ltr]0.8∗255000=2040000.8∗255000=204000[/ltr]
and Susanne can use the rest of her money to bring it below $200000, making it possible to cover all costs. [color=#17b529]So, this house is possible.[/color]

Rumz1001