Answer: Liza invested $15000 at 3% and $30,000 at 4%
Step-by-step explanation:
Let x be the amount invested by Liza at 3% interest then the amount she invested in 4% interest will be 2x.
We know that the compound interest with principal P is give By
[tex]I=P(1+r)^n-P\\\Rightarrow\ I=P[(1+r)^n-1][/tex], where n is the number of period.
Now, interest earned in 3% (in decimal 0.03) account in 1 year is given by:-
[tex]I_1=x[(1+0.03)^1-1]\\\Rightarrow\ I_1=x[0.03]\\\Rightarrow\ I_1=0.03x[/tex]
Similarly, interest earned in 4% (in decimal 0.03) account in 1 year is given by:-
[tex]I_2=2x[(1+0.04)^1-1]\\\Rightarrow\ I_2=2x[0.04]\\\Rightarrow\ I_2=0.08x[/tex]
According to the question,
[tex]I_1+I_2=1650\\\Rightarrow\ 0.03x+0.08x=1650\\\Rightarrow\ 0.11x=1650\\\Rightarrow\ x=15000[/tex]
Also, 2x=2(15000)=30000
Therefore, Liza invested $15000 at 3% and $30,000 at 4% .
