aleksandra tomich invested $14,724, part at 6% simple interest and part at 2% simple interest for a period…

aleksandra tomich invested $14,724, part at 6% simple interest and part at 2% simple interest for a period of 1 year. how much did she invest at each rate if each account earned the same interest? aleksandra invested $ at 6% and $ at 2%

aleksandra tomich invested $14,724, part at 6% simple interest and part at 2% simple interest for a period of 1 year. how much did she invest at each rate if each account earned the same interest? aleksandra invested $ at 6% and $ at 2%

Answer

Explanation:

Step1: Let the amount invested at 6% be $x$.

Then the amount invested at 2% is $(14724 - x)$. The simple - interest formula is $I=Prt$. Since $t = 1$ year, the interest from the 6% account is $I_1=0.06x$ and the interest from the 2% account is $I_2 = 0.02(14724 - x)$.

Step2: Set the two interests equal.

$0.06x=0.02(14724 - x)$

Step3: Expand the right - hand side.

$0.06x=0.02\times14724-0.02x$ $0.06x = 294.48-0.02x$

Step4: Add $0.02x$ to both sides.

$0.06x + 0.02x=294.48$ $0.08x=294.48$

Step5: Solve for $x$.

$x=\frac{294.48}{0.08}=3681$

Step6: Find the amount invested at 2%.

The amount invested at 2% is $14724 - 3681=11043$.

Answer:

Aleksandra invested $3681$ at 6% and $11043$ at 2%.