Since investment doubles in 70/r years, then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).

Answer: A.
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I think without the 1st sentence, we still can guess the answer easily.

$5,000 at 8%/year = $400/year --> 10-years interest will be $4,000, 20 years will be $8,000
Since the interest compounded annually in 18 years (very long period), the total value would be >$18,000 --> eliminate B,C,D,E

5000 will multiply approx. 4 times = 5000 * 4 = 20000

Answer = A
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Hi ColdSushi,

GMAT Quant questions (and the accompanying answer choices) are always carefully written. Sometimes they offer hints as to how you can use estimation to get to the correct answer.

Here, the word 'approximate' in the prompt is essentially telling you to estimate an answer. With an interest rate of 8% and the given formula, you're meant to estimate that the investment will double in 70/8 = about 9 years. The question then asks for the total investment after 18 years. THAT number (18) is not an accident - it was specifically chosen so that you can take advantage of your estimation.

Start = $5000
After 9 years = $10,000
After 18 years = $20,000

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Maybe because they said approximate and that they gave 70/r to help. Otherwise, goodluck computing a power of 18 without a calculator
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Although this question appears as if we may have to do a lot of calculating, we actually do not. Focus on the first sentence of the question stem. We are given that if money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. We are then given that Pat’s parents invest $5,000 at 8 percent interest. It follows that the investment will double after 70/8 years, which is roughly 9 years. With an initial investment of $5,000, the investment will double to $10,000 in about 9 years. In another 9 years (a total of 18 years) the investment will double again to about $20,000.

Answer A
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The question asks to find the approximate total amount of the investment in 18 years. So, (initial investment) + (interest earned in 18 years). If you use interests formula it's \(5000(1+0.08)^{18} \approx 19,980\). The question also gives a way to calculate this quicker by saying that "if money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years", which all the solutions above used to get the answer.
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GIVEN: At r percent interest, the amount of the investment will double in approximately 70/r years
So, at 8 percent interest, the time for the investment to double = 70/8 ≈ 9
So, the investment will double every 9 years

We can now create a growth table:
Initially, the investment is worth $5,000
After 9 years, the investment is worth $10,000
After 18 years, the investment is worth $20,000

Answer: A

Cheers,
Brent
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