Zach is planning to invest up to $50,000 in corporate and municipal bonds. The lest he will invest in corporate bonds is $6000 and he does not want to invest more than $27,000 in corporate bonds. He also does not want to invest more than $34,650 in municipal bonds. The interest is 8.5% on corporate bonds and 6.8% on municipal bonds. This is simple interest for one year. What is the maximum income?
Well50k-27k=23k
So since 8.5%interest is on Corp bonds
27000*.085=2,295
23,000*.068=1,564
3,859$ is the most he makes from interest
Since it says maximum income look at the maximum amount he count spend on the higher interest rate then subtract from the total he wants to spend. Since they are percentages I divide by 100 (8.5%/100= .085)
Hope this helps!
To find the maximum income, we need to determine the amount of money Zach will invest in corporate bonds and municipal bonds, and calculate the interest income for both.
Given:
- Zach will invest up to $50,000 in corporate and municipal bonds.
- The least he will invest in corporate bonds is $6000, and he does not want to invest more than $27,000 in corporate bonds.
- He does not want to invest more than $34,650 in municipal bonds.
- The interest rate is 8.5% on corporate bonds and 6.8% on municipal bonds, for one year.
To find the maximum income, we need to consider two scenarios: one where Zach invests the maximum allowed amount in corporate bonds and the rest in municipal bonds, and the other scenario where he invests the maximum allowed amount in municipal bonds and the rest in corporate bonds. We'll calculate the interest income for both scenarios and choose the higher one as the maximum income.
Scenario 1: Maximum investment in corporate bonds
- Zach will invest $27,000 in corporate bonds (maximum allowed).
- The interest rate for corporate bonds is 8.5%.
- Interest income from corporate bonds = $27,000 * 0.085 (8.5%) = $2,295.
Remaining investment for municipal bonds = $50,000 - $27,000 = $23,000.
- The interest rate for municipal bonds is 6.8%.
- Interest income from municipal bonds = $23,000 * 0.068 (6.8%) = $1,564.
Total maximum income for scenario 1 = $2,295 + $1,564 = $3,859.
Scenario 2: Maximum investment in municipal bonds
- Zach will invest $34,650 in municipal bonds (maximum allowed).
- The interest rate for municipal bonds is 6.8%.
- Interest income from municipal bonds = $34,650 * 0.068 (6.8%) = $2,356.
Remaining investment for corporate bonds = $50,000 - $34,650 = $15,350.
- The interest rate for corporate bonds is 8.5%.
- Interest income from corporate bonds = $15,350 * 0.085 (8.5%) = $1,304.75.
Total maximum income for scenario 2 = $2,356 + $1,304.75 = $3,660.75.
Comparing the two scenarios, we can see that scenario 1 has the higher maximum income of $3,859.
Therefore, the maximum income Zach can earn is $3,859.
To find the maximum income, we need to determine the maximum amount Zach can invest in each type of bond and then calculate the interest earned.
Let's start with the corporate bonds:
The least Zach will invest in corporate bonds is $6000.
He does not want to invest more than $27,000 in corporate bonds.
Therefore, Zach can invest any amount between $6000 and $27,000 in corporate bonds.
Next, let's consider the municipal bonds:
Zach does not want to invest more than $34,650 in municipal bonds.
Now, let's calculate the maximum income:
First, calculate the interest earned on the corporate bonds:
Maximum investment in corporate bonds = $27,000 (as per Zach's limit)
Interest earned from corporate bonds = Maximum investment * Interest rate
= $27,000 * 8.5% (converted to decimal form)
= $2,295
Next, calculate the interest earned on the municipal bonds:
Maximum investment in municipal bonds = $34,650 (as per Zach's limit)
Interest earned from municipal bonds = Maximum investment * Interest rate
= $34,650 * 6.8% (converted to decimal form)
= $2,355.20
Therefore, the maximum income from both types of bonds is the sum of the interest earned from corporate bonds and municipal bonds:
Maximum income = Interest earned from corporate bonds + Interest earned from municipal bonds
= $2,295 + $2,355.20
= $4,650.20
Therefore, the maximum income Zach can earn is $4,650.20.