Respuesta :
Answer:
Business-equipment loan, A=$15000
Small-business loan, B=$24000
home-equity loan, C= $39000
Step-by-step explanation:
Let the Business-equipment loan at an interest rate of 11%=A
Let the small-business loan was at an interest rate of 5% =B
Let her home-equity loan was at an interest rate of 4.5%.=C
Since her total Loan=$78000
A+B+C=78000....(I)
Simple Interest = (P X R X T)/100
Since the Time, T=1 year
Interest on A = 0.11A
Interest on B = 0.05B
Interest on C = 0.045C
The total simple interest due on the loans in one year was $4605.
0.11A+0.05B+0.045C=4605....(II)
The annual simple interest on the home-equity loan was $105 more than the interest on the business-equipment loan.
0.045C = 0.11A +105...(III)
We proceed to solve the simultaneous equations.
A+B+C=78000....(I)
0.11A+0.05B+0.045C=4605....(II)
0.045C = 0.11A +105...(III)
From (III), 0.045C = 0.11A +105
Substitute 0.045C = 0.11A +105 into (II).
0.11A+0.05B+0.11A +105=4605
0.22A+0.05B=4500
From (III),
[TeX]C=\frac{22A}{9}+\frac{7000}{3}[/Tex]
Substitute into (I)
[TeX]A+B+\frac{22A}{9}+\frac{7000}{3}=78000[/Tex]
[TeX]\frac{31A}{9}+B=78000-\frac{7000}{3} [/Tex]
[TeX]\frac{31A}{9}+B=\frac{227000}{3} [/Tex]
[TeX]\frac{31A+9B}{9}=\frac{227000}{3} [/Tex]
3(31A+9B)=9 X 227000
31A+9B=681000
0.22A+0.05B=4500 (Multiply by 9)
31A+9B=681000 (Multiply by 0.05)
1.98A+0.45B=40500
1.55A+0.45B=34050
Subtracting
0.43A=6450
A=$15000
From (III)
[TeX]C=\frac{22A}{9}+\frac{7000}{3}[/Tex]
[TeX]C=\frac{22X15000}{9}+\frac{7000}{3} =39000 [/Tex]
C=$39000
from (I)
A+B+C=78000
15000+B+39000=78000
B=$24000
