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

Answer = C = $5p and $10p

Min limit \(= (1 + \frac{86}{100})^3 = (1 + 0.86)^3 = 1.86^3 =\) Below 8

Max limit \(= (1 + \frac{109}{100})^3 = (1 + 1.09)^3 = 2.09^3 =\) Above 8

Nice problem! I think the whole xn business is just a tricky way of saying this is a compound interest problem.

Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p.

2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate.
1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound.

So range is 5p to 10p.
Answer C.

At the beginning of year 1, an investor puts p dollars into an investment whose value increases at a variable rate of x_n% per year, where n is an integer ranging from 1 to 3 indicating the year. If 85 \lt x_n \lt 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

The min. value for Xn for 1, 2 & 3 year can be 86%, 87% & 88% ( They can be as close to 85 as possible but for simplicity i am taking these rate and carefull about variable so cannot take all value same)
similarly Max value can be 109%, 108% & 107%
Now consider p 100
than solve by increasing it by saubsequent rate for both max and min for
for min rate it will be around 546 and for max it will be around 816 that is the range of final value and by puting p=100 in option u will get option C as the range.

One question...How do we know that they are talking about compound interest and not simple interest?

Even i have the same query as ShashankDave

Bunuel ,can you please clarify the below query

How to know whether they are talking about simple interests or compound interests?
Is it because the problem says, "an investment whose value increases at a variable rate of Xn"?

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