To buy both a new car and a new house, Tina sought two loans totalling $78,825. The simple interest rate on the first loan was 0.2%, while the simple interest rate on the second loan was 5.0%. At the end of the first year, Tina paid a combined interest payment of $2817.23. What were the amounts of the two loans?

Question

To buy both a new car and a new house, Tina sought two loans totalling $78,825. The simple interest rate on the first loan was 0.2%, while the simple interest rate on the second loan was 5.0%. At the end of the first year, Tina paid a combined interest payment of $2817.23. What were the amounts of the two loans?

Answer 1

Let the two loan amounts be X and Y.

X + Y = 78,825
0.002X + 0.05Y = 2817.23

Solve those two simultaneous equations.
Multiply both sides of the second equation by 20.

0.04x + Y = 56,344.60

0.96 X = 22,480.40
X = 23,417.08
Y = 55,407.92

Answer 2

Let's assume the amount of the first loan is x dollars, and the amount of the second loan is y dollars.

We know that the simple interest for the first loan is given by the formula: Interest = Principal * Rate * Time

The simple interest for the first loan can be calculated as: (x * 0.2% * 1) = 0.002x

The simple interest for the second loan can be calculated as: (y * 5.0% * 1) = 0.05y

According to the given information, Tina paid a combined interest payment of $2817.23 at the end of the first year. So, we can set up the following equation:

0.002x + 0.05y = 2817.23 ---(1)

Also, we know that the total loan amount is $78,825. So, we have another equation:

x + y = 78825 ---(2)

Now, we can solve these two equations simultaneously to find the values of x and y.

From equation (2), we can solve for x:

x = 78825 - y

Substituting this value of x into equation (1), we get:

0.002(78825 - y) + 0.05y = 2817.23

Simplifying the equation:

157.65 - 0.002y + 0.05y = 2817.23

Combining the like terms:

0.048y = 2659.58

Dividing both sides by 0.048, we get:

y = 55408.75

Substituting this value of y back into equation (2), we can solve for x:

x + 55408.75 = 78825

x = 78825 - 55408.75

x = 23416.25

So, the amounts of the two loans are $23,416.25 and $55,408.75, respectively.

Answer 3

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.