Answer: $16000 should be invested in the 4.25% bond.
Step-by-step explanation:
Let x represent the amount that he should invest in the bond paying 4.25 % interest.
Let y represent the amount that he should invest in the bond paying 4.75% interest.
A total of $28,000 is invested in two municipal bonds that pay 4.25% and 4.75% simple interest. This means that
x + y = 28000
The formula for determining simple interest is expressed as
I = PRT/100
Considering the bond paying 4.25% interest,
P = $x
T = 1 year
R = 4.25℅
I = (x × 4.25 × 1)/100 = 0.0425x
Considering the bond paying 4.75% interest,
P = $y
T = 1 year
R = 4.75℅
I = (y × 4.75 × 1)/100 = 0.0475y
The investor wants an annual interest income of $1250 from the investments. it means that
0.0425x + 0.0475y = 1250 - - - - - - 1
Substituting x = 28000 - y into equation 1, it becomes
0.0425(28000 - y) + 0.0475y = 1250
1190 - 0.0425y + 0.0475y = 1250
- 0.0425y + 0.0475y = 1250 - 1190
0.005y = 60
y = 60/0.005
y = 12000
x = 28000 - 12000 = $16000
