Stuart pays back two student loans over a 4-yr period. one loan charges the equivalent of 3% simple interest and the other charges the equivalent of 5.5% simple interest. if the total amount borrowed was $24,000 and the total amount of interest paid after 4 yr is $3280, find the amount borrowed from each loan.

the amount of each loans are $4000 and $20000

Step-by-step explanation:

Let the amount borrowed for the first loan be $x

Let the amount borrowed for the second loan be $y

The formula for simple interest will be

I = PRT/100

Where

I is the interest

P= principal

R= rate

T = time in years

Considering the first loan x,

Principal = x

R = 3%

T = 4 years

I = (x × 3 × 4)/100

Ix = interest on x

Ix= 12x/100

Considering the second loan y,

Principal = y

Rate = 5.5 %

T = 4 years

Iy = interest on y

Iy = (y × 5.5 × 4)/100 = 22y/100

If the total amount borrowed was $24,000, it means that

x + y = 24000

the total amount of interest paid after 4 yr is $3280. This means that

Ix + Iy = 3280. Therefore

12x/100 + 22y/100 = 3280

Cross multiplying,

12x + 22y = 3280 × 100 = 328000

12x + 22y = 328000

Substituting x = 24000 - y into 12x + 22y = 328000, it becomes

12(24000 - y ) +22y = 328000

288000 - 12y + 22y = 328000

- 12y + 22y = 328000 - 288000

10y = 40000

y = 40000/10 = $4000

x = 24000 - y = 24000 - 4000

x = $20000

step-by-step explanation:

i think the answer would be c