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hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Tue Aug 19, 2014 8:09 am

Can someone please explain the what question meant?

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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Source: Beat The GMAT — Problem Solving | Tue Aug 19, 2014 8:09 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Aug 19, 2014 8:58 am

hemant_rajput wrote:

Can someone please explain the what question meant?

First Mortgage = (80/100) x 320,000 = 256,000
Second Mortgage = (20/100) x 320,000 = 64,000

Interest on first mortgage = (4/100) x 256,000 = 10240
Interest on Second mortgage = (9/100) x 64,000 = 5760

Total Interest Payment = 16000 Per annum
Total Interest Payment Per Month = 16000/12 = 1333.33

Answer: Option A

Last edited by GMATinsight on Tue Aug 19, 2014 9:13 am, edited 1 time in total.

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Katy_: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun Aug 17, 2014 6:53 am; Thanked: 1 times

by Katy_ » Tue Aug 19, 2014 9:08 am

But there're no option for 1333.33 ? There's only 13,333 (?!)

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Aug 19, 2014 9:10 am

Katy_ wrote:But there're no option for 1333.33 ? There's only 13,333 (?!)

There is a word 'APPROXIMATELY' in the Question...

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Katy_: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun Aug 17, 2014 6:53 am; Thanked: 1 times

by Katy_ » Tue Aug 19, 2014 9:17 am

no I mean, 1333.33 has 3 number "3" while 13,333 has 4 number "3" (???!) Did I misunderstand something?

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Aug 19, 2014 9:19 am

Katy_ wrote:no I mean, 1333.33 has 3 number "3" while 13,333 has 4 number "3" (???!) Did I misunderstand something?

Option A is 1333

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Katy_: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun Aug 17, 2014 6:53 am; Thanked: 1 times

by Katy_ » Tue Aug 19, 2014 9:23 am

Oh I got it already. Thank you so much!

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Aug 19, 2014 12:15 pm

A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $320,000, 80% of which was in the first mortgage, what is her APPROXIMATE monthly interest payment?

A) $1,333
B) $1,733
C) $3,466
D) $13,333
E) $20,796

Another approach is to use some ESTIMATION and NUMBER SENSE.

Given:
80% of $320,000 at 4% interest rate
20% of $320,000 at 9% interest rate

Since MOST (80%) of the mortgage is at 4% interest rate, let's see what would happen if 100% of the $320,000 mortgage was at the 4% interest rate.
To make it easier to calculate, let's round the mortgage down to $300,000

4% of $300,000 = $12,000, so this is the ANNUAL interest payment.
This translates into $1000/month.
Now if we had factored in the fact that 20% of the mortgage is charged 9% interest AND the fact that we should have used $320,000 (rather than $300,000), what effect would this have on the $1000/month interest payment?

If we have a strong number sense, we will have a general feeling that the interest payment is a BIT BIGGER than $1000/month.

So, choose A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Aug 19, 2014 12:29 pm

A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $320,000, 80% of which was in the first mortgage, what is her APPROXIMATE monthly interest payment?

A) $1,333
B) $1,733
C) $3,466
D) $13,333
E) $20,796

Here's another approach that uses some ESTIMATION and NUMBER SENSE.

Given:
80% of $320,000 at 4% interest rate
20% of $320,000 at 9% interest rate

Let's examine what would happen if HALF of the $320,000 were charged 4% interest, and HALF were charged 9% interest.

The result would be a COMBINED annual interest rate of 6.5%.
Now what is 6.5% of $320,000?
Hmmm, that's too much work.
Let's calculate 6% of $300,000 instead. This works out to ANNUAL interest payment of $18,000, which translates into $1500/month
So, using some NUMBER SENSE, we can conclude that 6.5% of $320,000 results in interest payments in the range of $1700-$1800/month

Of course, this is the resulting payments when HALF of the $320,000 are charged 4% interest, and HALF are charged 9% interest.
In actuality, 80% is at 4% and only 20% is at 9%. So, the monthly payments will be a fair bit LESS THAN $1700-$1800

So, choose A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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