two mutual funds returned a total of $3320. first fund returned 9%second, which had invested $1000 more, returned 2%. What was the orginal investment?

Question

I need help solving this! Please help!

Answer 1

Let P = the amount invested in the first fund

Then P+$1000 = the amount inverted in the second fund

 

The total amount invested = P + P + $1000 = 2P + $1000

 

Interest from first fund = P*(0.09)          where 0.09 is the decimal equivalent of 9%

 

Interest from second fund = (P+1000)*(0.02)      where 0.02 is the decimal equivalent of 2%

 

Total Interest = $3320 = (0.09)P + (0.02)P + 20

 

3300 = (0.11)P

 

$30,000 = P

 

The total amount invested = 2P + $1000 = $61,000

 

Check:

 

($30000)((0.09) = $2700

($31000)(0.02) = $620

 

$2700 + $620 = $3320

Answer 2

The following solution is incorrect, but i still keep it for learning purpose.

 

This problem can be solved by the system of two linear equations:

Let x represent the original investments into the first mutual fund, and y represents the original investment into the second mutual fund. Then at the moment of the return, the return from the first bank is x+x·0.09=1.09x, and the return from the second mutual fund is y+0,02y=1.02y

 

To make the system, we use the information that total return is 3320, and original investment into the second fund is 1000 more then into the first one. 

1.09x+1.02y=3320

y=x+1000

 

We solve the system by substitution method.

x=1090

y=2090

 

Now, all we need is to find the total original investment!

 

I just have noticed another tutor have solved this problem and have got a completely different answer. I checked the meaning "total return" and realized my mistake. "Total return" is the return on an investment, including income, dividends and interest. It does not include the original mount. 

I do not remove my post even though it is incorrect:). It is a good learning process. Thank you for Mr. Philip for covering my back! Great job!