You take out two loans. After 2 years, the total interest for the loans is $138. On the first loan, you pay 7.5% simple annual interest on a principal of $800. On the second loan, you pay 3% simple annual interest. What is the principal for the second loan?
800 * .075 * 2 + x * .03 * 2 = 138
120 + .06x = 138
.06x = 18
x = 300
To find the principal for the second loan, let's first calculate the interest paid for each loan.
For the first loan:
Principal = $800
Rate = 7.5%
Time = 2 years
To calculate the interest for the first loan, we use the formula:
Interest = Principal × Rate × Time
Interest = $800 × 7.5% × 2
Interest = $120
Now, let's calculate the interest for the second loan.
Total interest for both loans = $138
Interest for the first loan = $120
To find the interest for the second loan, we subtract the interest of the first loan from the total interest.
Interest for the second loan = Total interest - Interest for the first loan
Interest for the second loan = $138 - $120
Interest for the second loan = $18
The rate for the second loan is given as 3%.
Let's use the interest formula to find the principal for the second loan.
Interest = Principal × Rate × Time
$18 = Principal × 3% × 2
To find the principal, we divide both sides of the equation by (3% × 2):
Principal = $18 / (0.03 × 2)
Principal = $18 / 0.06
Principal = $300
Therefore, the principal for the second loan is $300.