A sum of money doubles itself at a compound interest in 15 years. In

Question

A sum of money doubles itself at a compound interest in 15 years. In how may years it will become 8 times ??

A. 30 years

B. 40 years

C. 45 years

D. 50 years

E. 60 years

PareshGmat · Accepted Answer

Say initial amount = 100

Final amount = 800

100 >>>>>>>> 200 >>>>>>>>> 400 >>>>>>>>>> 800

........... 15 ............ 15 ................. 15

Total = 15*3 = 45

Answer = C

unceldolan · Answer

Let's say amount of money = $2, then 8 times = 16 $

Then
Year 00 = 2 $
Year 15 = 4 $
Year 30 = 8 $
Year 45 = 16 $ --> this is our answer, hence C.

Nunuboy1994 · Answer

If the lump sum is 8x then this represents a 2x^3 increase to

x(1 +r)^15(3)= 8x

Thus
 "C"

Bunuel · Answer

If the sum doubles (*2) in 15 years, then it to become 2*2*2 = 8 times as large it should double three times, so three 15 years time period are needed, which is 3*15 = 45 years.

Answer: C.

njnikhiljindal567 · Answer

We can use the standard Compound interest formula for this -

let x be the amount of money invested

2x = x(1+ r/100)^15........................eq 1

Now to want to find the how much time it will take for 8x

Which is (eq1)^3

Hence 8x = x(1 +r/100)^ 45

Hence C

exc4libur · Answer

a(1+r)^{(15)}=2a…(1+r)^{(15)}=2…(1+r)=2^{(1/15)} 
 (1+r)^x=8…(2^{(1/15)})^{x}=8…2^x=8^{(15)}…2^x=(2^3)^{(15)}…x=3•15=45

Answer (C)

Farina · Answer

Amount will be doubled in every 15 years
Let the initial amount is 100
so in 15 years it will be 100 * 2 = 200
in next 15 years it will be 200 * 2 = 400
and again in 15 years it will be 400 * 2 = 800

so 15+15+15 = 45 years Option C

ScottTargetTestPrep · Answer

Solution:

If it takes 15 years to double the amount of an investment, then it takes another 15 years (or a total of 30 years) to double it again, making it 4 times the original amount. Finally, it takes another 15 years (or a total of 45 years) to double it again, making it 8 times the original amount.

Answer: C

Adnan123 · Answer

Principal = 2P when r = r, t = 15 years 
P (1 + r%)^15 = 2P
(1 + r%)^15 = 2

P = 8P, r = r, t = ?
P (1 + r%)^t = 8P
(1 + r%)^t = 8
take cube roots on both sides
(1 + r%)^(t/3) = 2

t/3 = 15
t = 45 Ans

luisdicampo · Answer

Deconstructing the Question

The investment  doubles in 15 years . 
We need the time for the investment to become  8 times  the original amount.

Step-by-step

Note:

8 = 2^3

So the amount must double  three times .

Each doubling takes:

15 	ext{ years}

Total time:

3 	imes 15 = 45

Answer: 45 years

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