Torres invested $P in a long term investment plan for 24 years at an i

Question

Torres invested $P in a long term investment plan for 24 years at an interest compound annually. But due to some financial issues he had to withdraw money at the end of 6 years.How much more amount could he have gotten after 24 years if he received $3P after 6 years , if it's known that there were no pre-closing charges or deductions in the plan?

A. 9P
B. 12P
C. 72P
D. 78P
E. 81P

A. 9P
B. 12P
C. 72P
D. 78P
E. 81P

GMATRockstar · Accepted Answer

This question is tricky at first since we don't know the compounding interest rate, and feels like perhaps we would need a compound interest formula to solve, but let's consider.

It started at P and then compounded 6 times and tripled itself to 3P. So this is more like a Geometric sequence question!

The rule is "P triples every 6 years."

Year 1 - P
Year 6 - 3P
Year 12 - 9P
Year 18 - 27P
Year 24 - 81P

How much more means we subtract 3P from 81P:
81P-3P = 78P

The answer is (D). This is an interesting question -- a sequence in disguise!

DHAR · Answer

Solution:  
P is the term initially invested. Torres gets 3P after 6 years.We need to find what  more  amount could he have gotten after 24 years.
Let’s arrange the data:
Amount Time
? 24
P 0
3P 6
3P*3 12
3P*3*3 18
3P*3*3*3 24
 =  81P 
Therefore, more amount Toress would have got= 81P-3P= 78P

FillFM · Answer

Option D

6y: P > 3P
12y: 3P > 9P
18y: 9P >27P
24y: 27P > 81P

81P - 3P = 78P

gmatway · Answer

24 years / 6 years as every 6 years the investment becomes thrice of the investment . So we get 24/6 = 4 intervals .

Now,
P$ ---------3P$ (1-6 YEARS)
3P$--(*3)--9P& (6-12 YEARS)
9P$--(*3)--27P$ (12- 18 YEARS)
27P$-(*3)--81P$ (18- 24 YEARS)

NOW How much more amount could he have gotten after 24 years , simply find difference between the amt he received and the final amt which he would have received after 24 years = 3P$ -81P$ = 78$ ,

ANSWER IS D

ishita27 · Answer

Let the rate of interest be X%
3P = P( 1+X% )^6
3 = ( 1+X% )^6

Let A be amount after 24 years
A = P( 1+X% )^24
A = P(( 1+X% )^6)^4
A = P( 3 )^4
A = 81P

So
81P - 3P = 78P

So Torres would have gotten 78P more if he would have invested for 24 years

Correct answer is D

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Torres invested $P in a long term investment plan for 24 years at an i

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