Expert: Pawan Musale - 8/26/2009

Question
You invest $25,000. Part of it earns 14%and part of it earns 16% interest. What is the most you can invest  
earning 14%  interest to earn $3600?  The answer is $20,000.  How was it solved?

Answer
Karen,

Total investment is 25,000. Consider that x amount is invested in 14% interest. So amount invested in 16% interest would be (25000 - x).

Now let us calculate interests on these individual investments:

14% on x amount gives interest of (14/100) * x
16% on (25000-x) amount gives interest of (16/100) * (25000 - x)

Total interest earned is 3600.

From all the three statements above,

Total interest is,

3600 = (14/100) * x + (16/100) * (25000 - x)
3600 = 0.14x + 0.16(25000 - x)
3600 = 0.14x + 4000 - 0.16x
0.16x - 0.14 = 4000 - 3600
0.02x = 4000

Hence,
x= 4000 / 0.02 = 20000

But x is nothing but the amount invested in 14% interest.

Hence the answer is $20000.

I believe this clarifies your concern.

Kindly let me know if anything is not clear.

All the best.

Regards,
Pawan