" 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?"
$1900/$32000=5.9375%
Amount invested in 5.75% bond
=$32000*(6.25-5.9375)/(6.25-5.75)
=$20,000
To determine the amount to be invested in the 5.75% bond, we can set up a system of equations based on the given information.
Let's denote the amount invested in the 5.75% bond as x.
According to the problem, the total investment is $32000, so the amount invested in the 6.25% bond would be 32000 - x.
Now, let's calculate the annual interest income from each investment. The formula for simple interest is I = P * r * t, where I is the interest, P is the principal (amount invested), r is the interest rate, and t is the time (in years).
For the investment in the 5.75% bond, the interest would be x * 0.0575 (5.75% as a decimal) since the interest rate is given as 5.75%. Since we want an annual interest income of $1900, we can set up the equation:
x * 0.0575 = 1900
Next, for the investment in the 6.25% bond, the interest would be (32000 - x) * 0.0625 (6.25% as a decimal). Again, we want an annual interest income of $1900, so we can set up the equation:
(32000 - x) * 0.0625 = 1900
Now, let's solve this system of equations to find the value of x, which represents the amount invested in the 5.75% bond.
First, simplify the equations:
0.0575x = 1900
0.0625(32000 - x) = 1900
Next, solve the equations:
0.0575x = 1900
x = 1900 / 0.0575
x ≈ $33043.48
Therefore, approximately $33,043.48 should be invested in the 5.75% bond.