Let the amount partially invested out of $21,020 be x for 12% annual interest;
So, the interest gotten from this investment is;
[tex]\begin{gathered} I=\frac{12x}{100} \\ \text{But A=P+I} \\ \text{Where P is the amount invested, A is the amount and I is the interest} \end{gathered}[/tex]Thus the amount from this investment is;
[tex]\begin{gathered} A=\frac{12x}{100}+x \\ A=1.12x \end{gathered}[/tex]Thus, the rest of the money after x has been invested is;
[tex]21020-x[/tex]And since this money suffered a loss of 5%, we have the amount from this investment as;
[tex]\begin{gathered} A=(21020-x)-(\frac{5}{100}(21020-x)) \\ A=21020-x-1051+0.05x \\ A=19969-0.95x \end{gathered}[/tex]Thus, the total income from both investments is $2026.
Then, the total amount after both investments is;
[tex]21020+2026=23046[/tex]Then, we can get the money invested x at 12% annual interest as;
[tex]\begin{gathered} 23046=1.12x+19969-0.95x \\ 23046-19969=1.12x-0.95x \\ 0.17x=3077 \\ x=\frac{3077}{0.17} \\ x=18100 \end{gathered}[/tex]The money invested at 12% annually is $18100.
The amount invested at 5% loss is;
[tex]21020-18100=2920[/tex]The amount invested at 5% loss is $2920
