Chloe wants to invest a total of $39000 into 2 savings account, one paying 6% per year in interest and the other paying 9% per year in interest (a more risky investment). If after 1 year she wants the total interest from both accounts to be $2730. How much should she invest in each account.

Question

investment at the 6% simple interest?

investment at the 9% simple interest?

Answer 1

Po1*r1*t + Po2*r2*t = 2730.
Po1*0.06*1 + Po2*0.09*1 = 2730,
0.06Po1 + 0.09Po2 = 2730.
Eq1: 6Po1 + 9Po2 = 273,000,

Eq2: Po1 + Po2 = 39000.
Multiply Eq2 by -6 and Add:
+6Po1 + 9Po2 = 273000.
-6Po1 - 6Po2 = -234,000.
Sum: 3Po2 = 39,000, Po2 =
$13,000 Invested in acc. #2.

Po1 = 39,000-13,000 = $26,000 Invested in acc. #1.