A man is planning to invest up to $22,000in bank X or bank Y or both. He wants to invest at least $2,000 but no more than $14,000 in bank X. Bank Y doesn't insure more than a $15,000 investment so he will not invest no more than that in bank Y. The intrest in bank X is 6% and in bank Y it is 6 1/2% and this will be simple intrest for one year. How much should he invest in each bank to maximize his income? What is the maximum income?
Well, it seems like this man has quite the conundrum on his hands. Let's see if I can help him with some clownish calculations!
To maximize his income, the man should invest $14,000 in bank X because that is the maximum amount allowed. This leaves him with $8,000 to invest in bank Y.
Now, let's calculate the interest earned for each bank:
Interest from bank X = $14,000 * 6% = $840
Interest from bank Y = $8,000 * 6.5% = $520
To find the maximum income, we add the interest earned from each bank together:
Maximum income = $840 + $520 = $1,360
So, if the man invests $14,000 in bank X and $8,000 in bank Y, he can maximize his income to $1,360. Just remember, these calculations are for a year of simple interest.
Keep in mind that investing is a serious matter, so always consult with a financial advisor before making any decisions.
To maximize his income, we need to find the optimal investment amounts for bank X and bank Y.
Let's assume he invests $x in bank X and $y in bank Y.
Given the following conditions:
- He wants to invest at least $2,000 but no more than $14,000 in bank X, so we have 2000 ≤ x ≤ 14000.
- Bank Y doesn't insure more than a $15,000 investment, so we have y ≤ 15000.
- The total investment should not exceed $22,000, so we have x + y ≤ 22000.
Now, let's calculate the interest income from each bank:
Interest from bank X = (6/100) * x
Interest from bank Y = (6.5/100) * y
To maximize his income, the investment should include the maximum amount for which bank X offers a higher interest rate. In this case, bank X offers a higher interest rate for investments up to $14,000.
So, if he invests $14,000 in bank X, the remaining amount to invest in bank Y would be $22,000 - $14,000 = $8,000.
Therefore, he should invest $14,000 in bank X and $8,000 in bank Y to maximize his income.
The maximum income can be calculated as follows:
Interest from bank X = (6/100) * 14000 = $840
Interest from bank Y = (6.5/100) * 8000 = $520
Maximum income = Interest from bank X + Interest from bank Y = $840 + $520 = $1360.
To maximize his income, the man should invest $14,000 in Bank X and the remaining amount, $8,000, in Bank Y.
Here's the calculation:
1. First, let's calculate the interest income if he invests $14,000 in Bank X.
Interest income from Bank X = Principal x Interest Rate = $14,000 x 6% = $840.
2. Next, let's calculate the interest income if he invests $8,000 in Bank Y.
Interest income from Bank Y = Principal x Interest Rate = $8,000 x 6.5% = $520.
3. Finally, let's calculate the total maximum income:
Total maximum income = Interest income from Bank X + Interest income from Bank Y
= $840 + $520 = $1,360.
Therefore, the man should invest $14,000 in Bank X and $8,000 in Bank Y to maximize his income. The maximum income he can earn is $1,360.