Compound Interest

[talaangoshtari]

Hi,

how can we solve this problem without using the compound interest formula?

The number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

A)3
B)4
C)5
D)6

[GMATinsight]

Hi,

how can we solve this problem without using the compound interest formula?

The number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

A)3
B)4
C)5
D)6

Just play with numbers

e.g. Let 100 be the amount to be put out at 20%

0th Year 100
at the end of 1st year 120
at the end of 2nd year 144
at the end of 3rd year 172.8
at the end of 4th year 207

i.e. 4 years

Answer: Option B

[Matt@VeritasPrep]

Hi,

how can we solve this problem without using the compound interest formula?

The number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

A)3
B)4
C)5
D)6

Start with your initial investment x, then multiply by 1.2 each year to see what you've got.

End of year 1 = 1.2x
End of year 2 = 1.2 * 1.2x = 1.44x
End of year 3 = 1.2 * 1.2 * 1.2x = 1.728x
End of year 4 = 1.2 * 1.728x > 2x

So we've more than doubled our investment at the end of the fourth year.

[Brent@GMATPrepNow]

The number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

A)3
B)4
C)5
D)6

There's something called the Rule of 72 called that goes something like this:
If the annual interest rate is x percent, then the number of years for an investment to double is approximately 72/x

For example, if the interest rate is 9%, then the number of years for an investment to double is approximately 72/9. So, in ABOUT 8 years, the investment will double.

In the question, the interest rate is 20%, so the number of years for an investment to double = approximately 72/20 ≈ 3.6

Of course, this is an approximation, but it appears that answer choice B works here.

ASIDE: the Rule of 72 is NOT tested on the GMAT.
ASIDE: using logarithms (a concept that is not tested on the GMAT), the precise answer is 3.802 years.

Cheers,
Brent