An investor deposited $X into Account A and $(X + 400) into Account B. Account A pays a simple interest rate of 5% per annum, whereas Account B pays a simple interest rate of 12% per annum. If the aggregate interest accrued from Account A after 4 years and Account B after 3 years equals $704, calculate the value of X.

The correct answer is 1000.

Step 1: Calculate the interest accrued from Account A

The formula for calculating simple interest is:

$\text{Simple Interest}=\frac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}$

For Account A:

Principal = $$X$

Rate of interest = 5% per annum

Time period = 4 years

The interest accrued from Account A (${\text{Interest}}_{\text{A}}$) is:

${\text{Interest}}_{\text{A}}$

Step 2: Calculate the interest accrued from Account B

For Account B:

Principal = $$(X+400)$

Rate of interest = 12% per annum

Time period = 3 years

The interest accrued from Account B (${\text{Interest}}_{\text{B}}$) is:

${\text{Interest}}_{\text{B}}$

Expanding this expression:

${\text{Interest}}_{\text{B}}$

Step 3: Set up the total interest equation

The total aggregate interest from both accounts after the given periods equals $704:

${\text{Interest}}_{\text{A}}$

Substitute the derived interest expressions into the total interest equation:

$0.20X+0.36X+144=704$

Step 4: Solve for X

Combine the terms involving $X$:

$0.56X+144=704$

Subtract 144 from both sides:

$0.56X=704-144$

$0.56X=560$

Divide both sides by 0.56:

$X=\frac{560}{0.56}$

$X=1000$

Thus, the value of $X$ is 1000.