To solve this problem, we'll use the formula for simple interest:
Interest = Principal * Rate * Time
Let's denote the amount of the first loan as x. Since the simple interest rate on the first loan was 0.2%, we can write the interest for the first year as:
Interest for first loan = x * 0.002 * 1
We can simplify this to:
Interest for first loan = 0.002x
Next, since the simple interest rate on the second loan was 5.0%, we can write the interest for the second loan as:
Interest for second loan = (78825 - x) * 0.05 * 1
We can simplify this to:
Interest for second loan = 0.05(78825 - x)
According to the given information, the combined interest payment after the first year was $2817.23. Therefore, we can set up the following equation:
0.002x + 0.05(78825 - x) = 2817.23
Now, let's solve this equation to find the value of x, which represents the amount of the first loan:
0.002x + 0.05(78825 - x) = 2817.23
0.002x + 3941.25 - 0.05x = 2817.23
-0.048x + 3941.25 = 2817.23
-0.048x = 2817.23 - 3941.25
-0.048x = -1124.02
x = -1124.02 / -0.048
x ≈ 23416.04
So, the amount of the first loan, x, is approximately $23,416.04.
To find the amount of the second loan, we subtract the first loan from the total sought amount:
Amount of second loan = 78825 - 23416.04
Amount of second loan ≈ 55408.96
Therefore, the amounts of the two loans are approximately $23,416.04 and $55,408.96.