A total of $42,000 is invested in two municipal bonds that pay 4.25% and 7.75% simple interest. The investor wants an annual interest income of $2765 from the investments. What amount should be invested in the 4.25% bond

$14,000 should be invested in the 4.25% bond.

Explanation:

Let's assume

Investment in bond with a coupon rate of 4.25% = x  

Investment in bond with a coupon rate of 7.75% = y

According to given condition

x + y = $42,000 (i)

4.25%x + 7.75%y = $2,765

or

0.0425x + 0.0775y = $2,765 (ii)

Multiplying the equiation (i) by 0.0425

0.0425x + 0.0425y = $1,785 (iii)

Subtracting equation (iii) from equation (ii)

0.0425x + 0.0775y =  $2,765

-0.0425x - 0.0425y = -$1,785

0 + 0.0350y = $980

0.0350y = $980

y = $980 / 0.0350

y = $28,000

Placing valye of y in equiation (i)

x + $28,000 = $42,000

x = $42,000 - $28,000

x = $14,000

Hence

Investment in bond with a coupon rate of 4.25% = x  = $14,000

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