If money is invested at r percent interest, compounded annua

Question

If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000

(A) $20000 
(B) $15000 
(C) $12000 
(D) $10000 
(E) $9000

PS16831

Bunuel · Accepted Answer

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.

KarishmaB · Answer

If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000

(A) $20000 
(B) $15000 
(C) $12000 
(D) $10000 
(E) $9000

There has to be a logic to why they gave you "If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years."

If r = 8%, the principal will double in 70/8 = apprx 9 years. So in 9 years, 5000 will become 10,000. In another 9 years (i.e. 18 years from now) principal will double again and become $20,000.

kshitij89 · Answer

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

MulanQ · Answer

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

ColdSushi · Answer

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.

EMPOWERgmatRichC · Answer

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:  A

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

EMPOWERgmatRichC · Answer

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:  A

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

JeffTargetTestPrep · Answer

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

dave13 · Answer

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

Bunuel · Answer

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.

BrentGMATPrepNow · 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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=nMvZBDAN1XE

ArnauG · Answer

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.

bagad.07 · Answer

OG Question Code: PS16831

Bunuel · Answer

________________________________
Thank you! Added to the first post.

lavanya.18 · Answer

70/8= 8.7 so approx. 9
divide 18 by 9= 2

5000 doubles twice, ie. 5000*2*2= 20,000

egmat · Answer

I see we're working through this compound interest problem. It might look complex at first, but there's actually a clever shortcut built right into the question that makes this much simpler than it appears.

Let's break this down together:

The problem gives you a golden rule: money doubles every  \frac{70}{r}  years when invested at  r % interest. This is your key to solving this quickly!

Step 1: Find the doubling time 
With  r = 8 % interest, your money doubles every:
 \frac{70}{8} = 8.75  years

Step 2: Count how many times the money doubles 
In 18 years, you'll have:
 \frac{18}{8.75} \approx 2.06  doubling periods

Notice how this is essentially 2 complete doublings? The 0.06 extra is so small we can ignore it for an approximation.

Step 3: Apply the doublings 
Starting amount: $5,000
After first doubling (8.75 years):  5,000 	imes 2 = 10,000 
After second doubling (17.5 years):  10,000 	imes 2 = 20,000

Since we're at approximately 18 years (just 0.5 years past the second doubling), and the question asks for an approximate value, our answer is  $20,000 .

The answer is  (A) .

---

Want to master this problem type systematically? You can check out the  step-by-step solution on Neuron by e-GMAT  where you'll discover the complete framework for handling compound interest problems, including time-saving techniques and how to recognize when exact calculations aren't needed. You'll also learn how this "Rule of 70" connects to other exponential growth problems you'll see on the GMAT. Plus, you can explore  hundreds of other official GMAT questions  with detailed explanations to build consistent accuracy across all question types.

totaltestprepNick · Answer

A https://www.youtube.com/watch?v=r1W0dhqwHw8 Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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