Interest Problems

Question: A man has $10,000  to invest, some in a relatively safe account, earning 5% interest per year, and the rest in more speculative investments earning 12% per year. If the total interest earned for the year was $955, how much was at each rate?

Solution: 

Let X be the amount invested at 5% interest per year

Let Y be the amount invested at 12% interest per year.

Total Investment 

X+Y=10000    ----->EQN (1)

Total Interest

5%X+12%Y=955      --------->EQN(2)

Multiply Eqn(2) with 100

5X+12Y=95500

EQN(2)-EQN(1) multiplied with 5

   5X+12Y=95500
-  5X-5Y=-50000

7Y=45500

Y=6500
ADD Y value in EQN(1)
X+6500=10000
X=3500

Therefore 3500 principal amount invested at rate of interest 5%
and 6500 is the principal amount invested at rate of interest 12%.
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Question: A woman invests at 6% and $3000 more than this at 9%.If the total interest earned per year is $4170, how much was invested at each rate.

Solution:

Let x be the amount invested at 6%.

	Amount	percent	Interest
6%	x	0.06	0.06*x
9%	X+3000	0.09	0.09*(x+3000)
Total			4170

Then the equation as follows

0.06x+0.09(x+3000)=4170
0.06x+0.09x+270=4170
0.15x=3900
x=26000 at 6%
x+3000=29000 at 9%

Verification:
26000(0.06)=$1560
29000(0.09)=$2610
                  --------------
                     $4170


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