OG13 PS Q31 - Interest

[gmatstud]

Q31 OG 13 PS)
Lucy invested 10,000 in a new mutual fund account exactly 3 years ago. The value of account increased by 10% during 1st year, increased by 5% during 2nd year and decreased by 10% during 3rd year. What is value of account today?

Here, my initial thought process was to assume that after 1 year, you add 10% to principal and then calculate 5% increase on total amount. However, OG does not treat it that way. It just looks at principal account only.

If you read question, "value of account increased", so for 2nd year, my assumption was that the value of account at end of 1st year was 11000 and then there was increase of 5% on this.

[tutorphd]

This is OG12 PS Q64.

I don't have OG13, but OG12 treats it in the correct way. The total for each year (original + change) is based on the total of the previous year:

before: 10000
end of first year total: (100% + 10%)10000 = (1.10)10000
end of second year total: (100%+5%)(1.10)10000 = (1.05)(1.10)10000
end of third year total: (100%-10%)(1.05)(1.10)10000 = (0.9)(1.05)(1.10)10000 = 10395

[gmatstud]

aah...ok..i misread the explanation of OG. So my assumption was right..it is similar to Compound Interest problem.

Thanks

[tutorphd]

Yes that is a very good observation: compound interest is applying consecutive percents with of the same value.