Source: Official Guide for the GMAT 13th Ed. Problem Solving; #31 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #31

1

Lucy invested $10,000 in a new mutual

Lucy invested $10,000 in a new mutual account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

3 Explanations

1

Chitrabhanu Dasgupta

On the calculation part:

1.1 * 1.05 * 0.9 * 10,000
= 0.99 * 1.05 * 10000
= 0.99 * 10500
=
10500
- 105
= 10395

Feb 7, 2016 • Comment

1

Isha ajmani

Net Change in Ist and IInd year = +10+5+ (10*5)/100 = 15.5
Net change in IInd and IIIrd year = +15.5-10 - (15.5*10)/100 = 3.95

So the amount of $10000 will increase by 3.95% over the three years.
Thus, the amount at the end of three years will be 10395.

Jul 15, 2014 • Comment

, Magoosh Tutor

Clever solution! :D

Jul 15, 2014 • Reply

4

Gravatar Mike McGarry, Magoosh Tutor

Dec 27, 2013 • Comment

Vidyasagar Mohan Ram

Can we multiply all the multipliers and then find the total value ?

Sep 14, 2015 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Vidyasagar :)

Great observation! Yes, because the order in which we multiply doesn't matter (this is the Commutative Property), we can find the final value by multiplying the product of the multipliers by the original value :)

In other words,

Final value = [product of multipliers]*[original value]

[(1.1)(1.05)(0.9)]*($10000) = $10395

Oct 17, 2015 • Reply

bilal muzaffar

bt Cydney Seigerman how to multiply all the decimal numbers without calculator, any simple way out?

Aug 28, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Bilal,

While we can multiply the values in any order, that's not necessarily the best approach. It looks like Chitrabhanu provides a straight forward way to do the calculation efficiently. First they multiplied

1.1*0.9 = .99

then

1.05*10000 = 10500

leaving us with

0.99*10500

Instead of finding this product directly, it's a faster calculation if we recognize that the product is 0.01 (1%) less than 10500. One percent of 10500 = 105, so

0.99*10500 = 10500 - 105 = 10395

Hope this helps!

Aug 29, 2016 • Reply

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