Question

Katie took out two loans for a total of $50,000, to pay off her trip to Europe. The rate of interest on the loans was 3% and 7%. After one year, her interest totaled $2700. How much did she put into the loan that offered a 3% interest rate?

a) $20,000
b) $30,000
c) $40,000
d) $10,000

Answer 1

Katie placed $20,000 into the loan with a 3% interest rate. This was calculated by setting up and solving a system of equations based on the given total amount of loans, the individual interest rates, and the total interest accrued in one year.

Step-by-step explanation:

The question relates to solving a system of equations based on simple interest formula to find the amount Katie put into the loan with a 3% interest rate. Using two loans totaling $50,000, with separate interest rates of 3% and 7%, and knowing that the total interest accrued in one year is $2,700, we can set up the following system of equations:

• Loan with 3% interest rate: 0.03x
• Loan with 7% interest rate: 0.07(50,000 - x)
• Total interest: 0.03x + 0.07(50,000 - x) = 2,700

By solving this equation, we can determine the amount placed in the loan with a 3% interest rate:

0.03x + 3,500 - 0.07x = 2,700
-0.04x = -800
x = $20,000

Hence, Katie put $20,000 into the loan with a 3% interest rate.