To buy both a new car and a new house, Tina sought two loans totalling $319,531. The simple interest rate on the first loan was 2.7%, while the simple interest rate on the second loan was 2.6%. At the end of the first year, Tina paid a combined interest payment of $8334.15. What were the amounts of the two loans
To find the amounts of the two loans, let's assume the principal amount of the first loan is x, and the principal amount of the second loan is y.
According to the problem statement, the total amount of the loans is $319,531:
x + y = $319,531 ---(1)
The interest on the first loan, at a rate of 2.7%, can be calculated as (principal amount * interest rate):
Interest on the first loan = x * 2.7% = 0.027x
Similarly, the interest on the second loan, at a rate of 2.6%, can be calculated as (principal amount * interest rate):
Interest on the second loan = y * 2.6% = 0.026y
At the end of the first year, Tina paid a combined interest payment of $8,334.15:
Interest on the first loan + Interest on the second loan = $8,334.15
0.027x + 0.026y = $8,334.15 ---(2)
We now have a system of two equations with two unknowns (x and y). We can solve this system to find the values of x and y.
To solve the system, let's use the method of substitution:
From equation (1), we have:
x = $319,531 - y
Substitute this value of x into equation (2):
0.027($319,531 - y) + 0.026y = $8,334.15
Solve the equation for y:
8640.837 - 0.027y + 0.026y = $8,334.15
0.001y = $8,334.15 - 8640.837
0.001y = $305.687
Divide both sides by 0.001 to isolate y:
y = $305,687
Now substitute this value back into equation (1) to find x:
x = $319,531 - $305,687
x = $13,844
Therefore, the amounts of the two loans are as follows:
The first loan is $13,844
The second loan is $305,687