The number of years it would take for the value of an investment to do

Question

The number of years it would take for the value of an investment to double, at 26% interest compounded annually, is approximately which of the following?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

DavidTutorexamPAL · Answer

As we're explicitly asked to estimate, we won't bother with exact calculations.
This is an Alternative approach.

If we start with 100 and increase every year by 25% (which is exactly 1/4 so easier to calculate than 26%)
after 1 year we'd have 100 + 100/4 = 125,
after 2 years we'd have 125 + 125/4 = about 125 + 30 = 155
after 3 years we'd have about 155 + 155/4 = about 155 + 40 = 195.
This is very nearly double what we started!

(B) is our answer.

Abhishek009 · Answer

A = P(1 + \frac{r}{100})^n

Or,  2p = p(1 + \frac{26}{100})^n

Or,  2 = (1 + \frac{26}{100})^n

Or,  2 = (\frac{126}{100})^n

Or,  2 = 1.26^n

Now calculate ,  1.26^2 = 1.5876

And  1.26^3 = 2.00 , Thus Answer must be (B) 3

generis · Answer

Agreed, estimation is the way to go. A compound interest rate of 26% translates into a multiplier of 1.26. Change to 1.25

1.25=1\frac{25}{100}=1\frac{1}{4}=\frac{5}{4}

Imagine 1 in an account.

Multiply  1*\frac{5}{4}*\frac{5}{4}*\frac{5}{4}  ... until the numerator is about twice the denominator.

Each time the multiplier   gets used  = 1 year has elapsed 
(the multiplier is being used at the  end  of each year, with a first year base of 1)

1*\frac{5}{4}*\frac{5}{4}*\frac{5}{4}=\frac{125}{64}  => 125 is  \approx  double 64

Number of years?  \frac{5}{4}  was used three times, i.e., at the end of each of 3 years

Answer B

Same as above with $1 and years shown

Begin:  $1=> End Year 1:  ($1*\frac{5}{4})=$\frac{5}{4}

Begin:  $\frac{5}{4}=> END Year 2: ( $\frac{5}{4}*\frac{5}{4})=$\frac{25}{16}

Begin:  $\frac{25}{16}=> END Year 3:  ($\frac{25}{16}*\frac{5}{4})=$\frac{125}{64}

$125  is just about double  $64

One more year? Check

Begin:   $\frac{125}{64}=> END Year 4: ($\frac{125}{64}*\frac{5}{4})=$\frac{625}{256}

MORE than doubled. (256*2 = 512). Too many years.

End of Year 3 was correct.

Answer B

EgmatQuantExpert · Answer

Given

• An amount is invested at 26% interest compounded annually.

To Find

• The Time taken for the sum to become double.

Approach and Working Out

• It will become 1.26 times after every year. 
 o So, we can simply multiply by this number to check when it becomes double. 
• Let the initial amount be 1.
 o After 1 year – 1.26
o After 2 years –  1.26^2  = 1.59
o After 3 years –  1.26^3  = 2

Correct Answer: Option B

ScottTargetTestPrep · Answer

Solution:
 
We can create the equation where the initial value of the investment is 100 and the final value is 200 and n is the number of years that doubles 100 to 200 at 26% interest rate compounded annually:

100(1 + 0.26)^n = 200

1.26^n = 2

Let’s approximate 1.26 as 1.25 or 5/4. Since (5/4)^3 = 125/64 ≈ 2, we see that n is approximately 3.

Alternate Solution:

The Rule of 72s can be used to approximate the answer. The Rule of 72s states that if you divide 72 by the annual interest rate, the quotient is the approximate doubling time. We see that if we approximate the given annual interest rate as 24%, then the division of 72 by 24 is 3; thus, the approximate number of years for the investment to double is 3 years.

Answer: B

KarishmaB · Answer

Note that in case of simple interest with a 26% rate of interest, it would take 4 years to double an investment. Since we are talking about compound interest here, and the rate of interest is very high, one can expect big increments in less time and hence if I had 30 secs for the question, I would guess 3 years and move on.

Answer (B)

If I did have some more seconds, I would say we need  (\frac{126}{100})^n  to become 2 which is hard to calculate. So instead I would approximate it as 125/100 = 5/4 and I know that  (\frac{5}{4})^3 = \frac{125}{64}  which is approximately 2.

sayan640 · Answer

KarishmaB   GMATinsight  I think the best method is to apply the rule of 72. 
72/ 26 almost equal to  3 ( or 2.7 ) . If we round 2.7 off , it will become 3. Hence the answer is 3.

KarishmaB · Answer

You can, if you know the rule of 72.

sayan640 · Answer

is there any case in which the rule of 72 does not apply ?  Bunuel

bumpbot · Answer

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The number of years it would take for the value of an investment to do

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