If money is invested at r percent interest, compounded annua

It's very important to pay attention to the wordings as first I thought that the compound interest formula needs to be applied.

Though I read the question again and got it correct

Posted from my mobile device

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

Hey all,

Just wondering what in the question made you realise you should solve this question via 5,000 x 2 x 2 rather than using the actual interest formula? i.e. P(1+r/n)^nt?

I used the formula then realised the calcs were too complicated.

Thanks in advance for your help.

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

Hi All,

This question has some similarities to "symbolism" questions (in which the prompt shows you a "made up" symbol, tells you what it means and asks you to do a simple calculation with it). The easiest way to tackle the question is to simply follow the instructions.

We're told that r = percent interest.

We're also told that an investment with DOUBLE in approximately 70/r years.

We're told to invest $5,000 at 8 percent for 18 years.

Plug in r = 8

70/8 is about 9 years, meaning our investment will DOUBLE in 9 years.

In the first 9 years, $5,000 doubles to $10,0000
In the next 9 years, $10,000 doubles to $20,000

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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

Bunuel isnt the question asking to calculate the total sum (invested ammound +interest rate) like this \(x = 5000(1+0.08)^9\) where doest say that we need to calculate only amount ivested i am kinda condused

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.

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

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

The investment will double in approximately 70/r years, where r is the annual interest rate. In this case, the interest rate is 8 percent, so we can calculate the doubling time as approximately 70/8 = 8.75 years.

Now, we need to determine the number of doubling periods within 18 years. Dividing 18 by the doubling time gives us 18 / 8.75 ≈ 2.057 doubling periods.

Since the investment doubles each period, after 2 doubling periods, the total amount will be 2 * 2 = 4 times the initial amount.

Therefore, the approximate total amount of the investment after 18 years is:

Total amount = 4 * $5,000 = $20,000

Hence, the answer is (A) $20,000.

OG Question Code: PS16831

________________________________
Thank you! Added to the first post.