A school must raise exactly $2,500 over the next year by investing a

Question

A school must raise exactly $2,500 over the next year by investing a total of $30,000 in stocks, which yield 9% annual interest, and bonds, which yield 8% annual interest. If the school wants to invest as much as possible in stocks, then how much should the school invest in stocks?

A. $1,000
B. $10,000
C. $20,000
D. $29,000
E. $30,000

A. $1,000
B. $10,000
C. $20,000
D. $29,000
E. $30,000

0akshay0 · Answer

let x be the amount to be invested in stocks 9x/100 + (8/100)*(30000-x) = 2500 9x + 240000 - 8x = 250000 x = 10000 Hence option B is correct Hit Kudos if you liked it 8-)

appu2693 · Answer

Could you please elaborate your approach?

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0akshay0 · Answer

The school must raise exactly $2,500 by investing as much as possible in stocks. I have assumed that amount to be x. Investment in stocks yields 9% therefore the returns from this investment = 9x/100 The remaining amount i.e. (30000-x) is invested in bonds, which yield 8% annual interest. i.e. (8/100)*(30000-x) The sum of the returns from both investments = 2500. So, 9x/100 + (8/100)*(30000-x) = 2500 x = 10000 therefore the school must invest 10000 in stocks to raise exactly $2,500 by investing as much as possible in stocks. appu2693 : Hope its clear Hit Kudos if you liked it 8-)

mjana89 · Answer

One of the quickest way to solve this problem is using allegation.

If whole amount is invested in stock, the return: $30000*9% = $2700
If whole amount is invested in bond, the return: $30000*8% = $2400
But the return needed is exactly $2500

See attachment.

Hence the total amount needs to be invested in stock and bond in the ratio 1:2.
Therefore amount invested in stock is $30000*(1/3) = $10000.

energetics · Answer

2,500 = a/100 * 30,000 
2,500/300 = a
8.33 = a, this is the interest we need get 2,500 from 30,000

1) Draw a number line:

8---8.3------9
B---Avg------S
 
We have 2 amounts, bonds at at 8% and stocks at 9% interest
If it was exactly half of each, it would be 8.5% ... while we have a = 8.3% 
The distance from 8 to 9 is 1, so we can say the ratio of the 'pull' of bonds on the average is 2/3 to the 'pull' of stocks at 1/3, or a ratio of 2:1. Since we're looking for stocks it would be 30,000 * 1/3 = 10,000

Or 2) Use weighted average formula: 
w1/w2 = Avg2 - Avg / Avg - Avg1
Bonds/Stocks = 90 - 83 / 83 - 80
B/S = 7/3 
so S = 3/10 * 30,000 = 9,000 (due to rounding... closest answer is B)

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A school must raise exactly $2,500 over the next year by investing a

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