Question

you invested $20680 part of it in a stock that paid 12% annual interest. However the rest of the money suffered a 5% loss. if the total annual income from both investments was $2026 how much was invested at each rate?​

Answer 1

Let x be the investment made at 12% annual interest and y be the rest of the investment that suffered a loss of 5%.

The initial total investment is $8000.

x
+
y
=
8000


In a year, 0.12x was earned while 0.05 was lost. The net income for both is $620.

0.12
x
−
0.05
y
=
620
0.12
x
−
0.05
(
8000
−
x
)
=
620
[
Substitute y using the first equation
]
0.12
x
−
400
+
0.05
x
=
620
0.17
x
−
400
=
620
0.17
x
=
1020
[
Add 400 to both sides
]
x
=
6000
[
Divide both sides by 0.17
]


The remaining investment is:

y
=
8000
−
(
6000
)
[
Substitute x value
]
y
=
2000


$6000 was invested in a stock that paid 12% annual interest while $2000 was invested on another investment that suffered a loss.