ming wang invested $10,000, part at 4% and part at 5% simple interest for a period of 1 year. how much was…

ming wang invested $10,000, part at 4% and part at 5% simple interest for a period of 1 year. how much was invested in each account if the interest earned in the 5% account was $248 greater than the interest earned in the 4% account?\nming wang invested $2800 at 4%.\nming wang invested $ at 5%.

ming wang invested $10,000, part at 4% and part at 5% simple interest for a period of 1 year. how much was invested in each account if the interest earned in the 5% account was $248 greater than the interest earned in the 4% account?\nming wang invested $2800 at 4%.\nming wang invested $ at 5%.

Answer

Explanation:

Step1: Let the amount invested at 4% be $x$.

Then the amount invested at 5% is $(10000 - x)$.

Step2: Calculate the interest from each account.

The interest from the 4% - account is $I_1=0.04x$ (using the simple - interest formula $I = Prt$, where $t = 1$ year). The interest from the 5% - account is $I_2=0.05(10000 - x)$.

Step3: Set up the equation based on the given condition.

We know that the interest earned in the 5% account was $248$ greater than the interest earned in the 4% account. So, $0.05(10000 - x)=0.04x + 248$.

Step4: Expand and solve the equation.

Expand the left - hand side: $500-0.05x = 0.04x+248$. Add $0.05x$ to both sides: $500=0.04x + 0.05x+248$. Combine like terms: $500=0.09x + 248$. Subtract 248 from both sides: $0.09x=500 - 248=252$. Divide both sides by 0.09: $x=\frac{252}{0.09}=2800$.

Step5: Find the amount invested at 5%.

The amount invested at 5% is $10000 - x$. Since $x = 2800$, the amount invested at 5% is $10000 - 2800=7200$.

Answer:

$7200$