Two accounts

Two accounts in the bank, one per year interest 2%, the second 3%. Total interest income 1900 USD. If we reversed interest rates, the yield would be USD 200 higher. What are the amounts on each account?

Correct answer:

a =  50000
b =  30000

Step-by-step explanation:


0.02a + 0.03b = 1900
0.03a + 0.02b = 1900+200

0.02·a + 0.03·b = 1900
0.03·a + 0.02·b = 1900+200

0.02a+0.03b = 1900
0.03a+0.02b = 2100

Pivot: Row 1 ↔ Row 2
0.03a+0.02b = 2100
0.02a+0.03b = 1900

Row 2 - 0.02/0.03 · Row 1 → Row 2
0.03a+0.02b = 2100
0.02b = 500


b = 500.00000001/0.01666667 = 30000.00000048
a = 2100-0.019999999999982b/0.03 = 2100-0.02 · 30000.00000048/0.03 = 49999.99999936

a = 49999.999999
b = 30000

Our linear equations calculator calculates it.



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