Answer:
The principal of the bank loan is $4,000
The principal of the federal lone is $14,000
Step-by-step explanation:
* Lets explain how to solve the problem
- Laura owes $18,000 on her student loans
- The interest rate on the bank loan is 2.5%
- The interest rate on the federal loan is 6.9%
- The total amount of interest she paid last year was $1,066
* Assume that the principle of the bank loan is $x and The principal of
the federal loan is $y
∵ Her loan is 18,000
∴ x + y = 18,000 ⇒ (1)
- The interest is I = PRT, where P is the principal, R is the rate of interest
in decimal ant is the time
# <u><em>The bank lone</em></u>
∵ P = $x
∵ R = 2.5/100 = 0.025
∵ T = 1
∴ <em>The interest of the bank lone</em> = x(0.025)(1) = <em>0.025 x</em>
# <u><em>The federal lone</em></u>
∵ P = $y
∵ R = 6.9/100 = 0.069
∵ T = 1
∴ <em>The interest of the federal lone</em> = 9(0.069)(1) = <em>0.069 y</em>
- The total interest is the sum of the interest of the bank lone and the
interest of the federal loan
∵ The total interest is $1,066
∴ 0.025 x + 0.069 y = 1,066 ⇒ (2)
* We have system of equations
- Multiply equation (1) by -0.025 to eliminate x
∴ -0.025 x - 0.025 y = -450 ⇒ (3)
- Add equations (2) and (3)
∴ 0.044 y = 616
- Divide both sides by 0.044
∴ y = 14,000
- Substitute value of y in equation (1) to find x
∴ x + 14000 = 18000
- Subtract 18000 from both sides
∴ x = 4000
∵ x represents the principal of the bake loan and y represents the
principal of the federal lone
* The principal of the bank loan is $4,000
* The principal of the federal lone is $14,000
