SOLUTION: Diffence between two loans is $10000, both loans have 5% annual interest rate. If the total interest is $2000 after one year how much was each loan?

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Question 30799: Diffence between two loans is $10000, both loans have 5% annual interest rate. If the total interest is $2000 after one year how much was each loan?
Answer by Fermat(136) About Me  (Show Source):
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Call the two loans L1 and L2. with L1 > L2
Then, L1 - L2 = 10,000
commom interest rate = 5%
I1 = interest on L1
I2 = interest on L2
I1 = %5*L1 = 0.05L1
I2 = %5*L2 = 0.05L2
I1 + I2 = 2000
.: 0.05L1 + 0.05L2 = 2000
0.05(L1 + L2) = 2000
dividing both sides by 0.05
L1 + L2 = 40,000 ----------------(1)
but
L1 - L2 = 10,000 ----------------(2)
adding (1) and (2),
2L1 = 50,000
L1 = 25,000
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L2 = 15,000
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