Question

Lake has a total of $10,000 to invest in two accounts. One account earns 1% simple interest, and the other earns 10% simple interest. How much should be invested in each account to earn exactly $280 at the end of 1 yr?

Part 1 of 2
$ should be invested in the 1% account.


Part 2 of 2
$ should be invested in the 10% account.

Answer 1

1. $8000 at 1%
2. $2000 at 10%

Explanation:

It often works well to let a variable represent the amount invested at the higher rate. Then an equation can be written relating amounts invested to the total interest earned.

__

setup

Let x represent the amount invested at 10%. Then 10000-x is the amount invested at 1%. The total interest earned is ...

0.10x +0.01(10000 -x) = 280

solution

Simplifying gives ...

0.09x +100 = 280

0.09x = 180 . . . . . . . subtract 100

x = 2000 . . . . . . divide by 0.09

10000 -x = 8000 . . . . amount invested at 1%

1.

$8000 should be invested in the 1% account

2.

$2000 should be invested in the 10% account