Answer:
The first loan L1 = $20,000
This is the loan with 3% simple interest
The second loan L2 = $4,000
This is the loan with 5.5% simple interest
Step-by-step explanation:
L1 + L2 = $24,000 ...(1)
4(3% of L1) + 4(5.5% of L2) = $3,280 ...(2)
Where the first term in equation (2) represents the total interest paid on loan 1 after 4 years
The second term represents total interest accruing to loan 2 after 4 years
From equation (1), we single out L1
L1 = 24,000 - L2
Substitute this value for L1 in equation (2)
288,000 + 10L2 = 328,000
L2 = $4,000
L1 = $24,000 - $4,000 = $20,000
Answer: 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
