At the beginning of year 1, an investor puts p dollars into

[chitrangada.maitra]

Source: mgmat
At the beginning of year 1, an investor puts p dollars into an investment whose value increases at a variable rate of x subscript n% per year, where n is an integer ranging from 1 to 3 indicating the year. If 85 < x subscript n < 110 for all n between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between

(A) $p and $2p
(B) $2p and $5p
(C) $5p and $10p
(D) $10p and $25p
(E) $25p and $75p

OA: C

The explanation uses the compound interest formula but the problem does not mention compound interest or cumulative etc. Is it standard to go with CI when nothing is mentioned?

[rajivbhatia2007]

Alternatively, I think you could think of the problem this way:

The lowest the investment value could be after three years is if it increased by 85% for each of the three years.

The highest the investment value could be after three years is if it increased by 110% for each of the three years.

The low end: 1.85 x 1.85 x 1.85 x p

The high end: 2.1 x 2.1 x 2.1 x p

The high end is slightly greater than 2^3, so 10 makes sense:

For the low end, 1.85 x 1.85 x 1.85 is definitely greater than 2 but definitely less than 10.

Therefore, only answer choice C works here.

my gmat story: http://gmathints.com/

[chitrangada.maitra]

where does the problem mention compound interest? It could be simple interest as well, right?

[gokul_nair1984]

The lowest the investment value could be after three years is if it increased by 85% for each of the three years.

The highest the investment value could be after three years is if it increased by 110% for each of the three years.

The low end: 1.85 x 1.85 x 1.85 x p

The high end: 2.1 x 2.1 x 2.1 x p

That's a great way to analyze Rajeev!

Chitrangada:

where does the problem mention compound interest? It could be simple interest as well, right?

Whenever the value of an investment increases per year at a given rate, this basically means Compound interest because the principal on which you derive interest keeps changing from year to year.

You could look at it in terms of Simple interest as well:

"At the beginning of year 1, an investor puts p dollars into an investment whose value increases at a variable rate of x subscript n% per year"

Analogy: Let's say you put in $10 and 10% interest rate in a bank.
(P+I) for the first year =(10*.1)+10=11
For the second year the interest will be calculated on the last principle of 11 and not on the initial principle of 10.--This is basically what your compound interest does in simple interest terms.
So (P+I) for second year will be=11+1.1=12.1

Makes Sense?

[tim]

Thanks, Gokul. Yes, you know it's compound interest because it tells you the percentage increase PER YEAR..