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Junior | Next Rank: 30 Posts
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by Koala » Sat Dec 18, 2010 9:47 am
Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage?

A) 6
B) 8
C) 10
D) 11
E) 13

From Veritas Prep Free Test ==> OA is B
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by beat_gmat_09 » Sat Dec 18, 2010 10:06 am
1st month - $100
2 - $300
3 - $900
4 - $2700
5 - $8100
6 - $24300
7 - $72900 ...... Total amount paid so far - 100+300+900+2700+8100+24300+72900 = $1093,00
8 - $218700 ...... total paid = $109300 + $218700 = $328000 (done)

No. of Months = 8
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by anshumishra » Sat Dec 18, 2010 11:31 am
Koala wrote:Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage?

A) 6
B) 8
C) 10
D) 11
E) 13

From Veritas Prep Free Test ==> OA is B
It forms a Geometric progression with :
a = 100
r = 3
S = 328000

Using the formula: S = a(r^n -1)/(r-1)

328000 = 100*(3^n-1)/2
=> 3^n = 6561 (Unit digit is 1)
=> n = 8 (How did I get that ? well, 3^4 = 81 ends in 1, so 3^4n will also end in 1 for all n, the only option here given was 8).

Thanks
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