A total of $32000 is invested in two municipal bonds that pay 5.75% and 6.25% simiple interest. The investor wants an annual interest income of $1900 from the investments. What amount should be invested in the 5.75% bond?
If the amount of money he invested at the 2muinicipal bond that pays 5.75% and 6.25% are m&n
Then
M+N=32000.....(*)
5.75%ofm and 6.25%of n
When you add them it must give him an interest of $1900
575m/10000+625n/10000=1900
575m+625n=19000000
Reduce by 25
23m+25n=760000.....(**)
You goal is to get m
So from (*)
N=32000-m
Plug "N" into (**)
23m+25(32000-m)=760000
23m+800000-25m=760000
-2m=760000-800000
-2m=-40000
m=$20000
To determine the amount to be invested in the 5.75% bond, we can set up a system of equations.
Let x be the amount invested in the 5.75% bond, then (32000 - x) would represent the amount invested in the 6.25% bond.
The formula for calculating simple interest is: Interest = Principal × Rate × Time
For the 5.75% bond, the interest earned would be 0.0575x, and for the 6.25% bond, the interest earned would be 0.0625(32000 - x).
The total annual interest income is given as $1900, so we have the equation:
0.0575x + 0.0625(32000 - x) = 1900
Now, we can solve for x:
0.0575x + 0.0625(32000 - x) = 1900
0.0575x + 2000 - 0.0625x = 1900
-0.005x + 2000 = 1900
-0.005x = 1900 - 2000
-0.005x = -100
x = -100 / -0.005
x = 20000
Therefore, $20,000 should be invested in the 5.75% bond.