An investor earns $1100 per year from bonds yielding returns of 4% and 5% each year. If the amounts at 4% and 5% were interchanged, she would earn $50 more per year. Find the total sum invested.

Answer 1

Let x be the amount invested at 4% and y be the amount invested at 5%. Then we have:

0.04x + 0.05y = 1100

0.05x + 0.04y = 1150

Multiplying the first equation by 0.05 and the second equation by 0.04, we get:

0.002x + 0.0025y = 55

0.002x + 0.0016y = 46

Subtracting the second equation from the first, we get:

0.0009y = 9

y = 10000

Substituting y = 10000 into the first equation, we get:

0.04x + 500 = 1100

0.04x = 600

x = 15000

Therefore, the total sum invested is:

x + y = 15000 + 10000 = 25000