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Compound interest and ratio

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Compound interest and ratio

by alltimeacheiver » Wed May 11, 2011 4:46 am
On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded
annually, and Lana invested $2,000 at 5 percent annual interest, compounded annually.
The total amount of interest earned by Tim's investment in the first 2 years was how
much greater than the total amount of interest earned by Lana's investment in the first 2
years?
A. $5
B. $15
C. $50
D. $100
E. $105


A certain company that sells only cars and trucks reported that revenues from car sales in
1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7
percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1
4
percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from
truck sales in 1996?
A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3
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by Brent@GMATPrepNow » Wed May 11, 2011 7:02 am
Please devote one post to one question :-)
It's difficult to follow the discussions when there are two (or more) questions posted in one thread.
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by GMATGuruNY » Wed May 11, 2011 9:48 am
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3
The following method is called alligation. It's an easy way to handle weighted average problems.

In the problem above, we want to combine an 11% decrease with a 7% increase to yield a total increase of 1%.
Thus, we need to know what ratio of (-11%) : (+7%) will yield a total increase of +1%.

The proportion needed of each starting percentage is the positive difference between the other 2 percentages.

Proportion needed of -11% = positive difference between the other 2 percentages = 7-1 = 6.
Proportion needed of 7% = positive difference between the other 2 percentages = 1-(-11) = 12.

Ratio of (-11%) : (+7%) = 6:12 = 1:2.

The correct answer is A.
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by pankajks2010 » Fri May 13, 2011 12:00 am
the algebraic approach to the second question would be as follows:

Let the car sales in 1996 be x and the truck sales be y

Now, as per the question, car sales in 1997 would be 0.89x and truck sales would be 1.07y and the total sales would become 1.01(x+y). The equation would become:

1.01(x+y)= 0.89x + 1.07y; solving this; 0.12x=0.06y; x/y=1/2.

PS: Somehow, I am unable to understand the alligation method (which saves time and avoids framing equations and the subsequent calculations) :(
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by finance » Fri May 13, 2011 2:25 am
alltimeacheiver wrote:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded
annually, and Lana invested $2,000 at 5 percent annual interest, compounded annually.
The total amount of interest earned by Tim's investment in the first 2 years was how
much greater than the total amount of interest earned by Lana's investment in the first 2
years?
A. $5
B. $15
C. $50
D. $100
E. $105
My answer is A. Think firstly only for the first year.Tim's interest income will be 100. So at the end of the year the value of the investment will me 1100. For the second year the interest income will be 1100*10%=110.Lana from the first year earns 2000*0.05=100 and for the second year 2100*0.05=105. The total amount of interest incomes differ by 5 dollars. What is the OA?
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