Question

Ralph chase graduated from college with a dept of $20000. He had taken out two different kinds of loans : a government loan at 3.3% APR ( annual percentage rate, or interest after one year) and a private loan at 4.9% APR . If his total interest after one year was $804 , how much money did he borrow from each source ?

Answer 1

Ralph borrowed $11,000 from the government source and $9,000 from the private source.

Explanation:

Let:

x = government loan

y = private loan

x + y = 20,000 ............................................ (1)

x = 20,000 - y ............................................. (2)

0.033x + 0.049y = 804 ............................ (3)

Substitute equation (2) into (3) for x, we have:

0.033(20,000 - y) + 0.049y = 804

660 - 0.033y + 0.049y = 804

0.016y = 804 - 660

0.016y = 144

y = 144 / 0.016 = $9,000

Substitute $9,000 for y in equation (2), we have:

x = 20,000 - 9,000 = $11,000

Therefore, Ralph borrowed $11,000 from the government source and $9,000 from the private source.