A total of $44,000 is invested in two municipal bonds that pay 5.75% and 7.25% simple interest. The investor wants an annual interest income of $2740 from the investments. What amount should be invested in the 5.75% bond

Amount invested at 5.75% = $30,000

Amount invested at 7.25% = $14,000

Explanation:

Let the amount invested

at 5.75% = X

at 7.25% = Y

According to given condition

X + Y = $44,000 (Eq 1)

and

0.0575X + 0.0725Y = $2,740 (Eq 2)

By multiplying (Eq 1) with 0.0575

0.0575X + 0.0575Y = $2,530 (Eq 3)

By subtracting (Eq 3) from (Eq 2)

0.0725Y - 0.0575Y = $2,740 - $2,530

0.015Y = 210

Y = 210 / 0.015

Y = $14,000

X + $14,000 = $44,000

X = $44,000 - $14,000

X = $30,000

Check:

$30,000 x 5.75% + $14,000 x 7.25% = $2,740

$2,740 = $2,740