Answer:
$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
<u>-0.0425x - 0.0425y = -$1,785</u>
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
