Suppose you have $9000 to invest and you invest part of it ($×) in a high risk venture at 11.5% per annum and the remainder with the bank at 4.5% per annum, both for one year.
1) write an algebraic expression for the amount of money invested at 4.5%
2) write an algebraic expression for the interest on ($×) at 11.5% for one year
3)write and simplify an expression for the total interest earned on the whole investment of $9000 after one whole year.
4) if you pay government tax on your interest at a rate fo 33 cents in the dollarwrite and simplify an expression for the amount of money that you receive from your interest after one year,after the tax is paid.
1. $(9000-x) @ 4.5%
2. 0.115*X
3. 0.115X + 0.045(9000-X).
0.115x + 405 - 0.045x
0.07x + 405.
4. 100% - 33% = 67% to Investor.
0.67(0.07x+405) = 0.047x + 19. = Amt.
received by investor.
1) The amount of money invested at 4.5% can be represented by the algebraic expression (9000 - $×).
Here's how you get this expression:
Given that you have $9000 to invest, and you invest a certain amount, $×, in the high-risk venture, the remaining amount invested in the bank is $9000 - $×.
2) The interest on ($×) at 11.5% for one year can be represented by the algebraic expression 0.115($×).
To derive this expression:
Multiply the investment amount ($×) by 0.115 (which represents 11.5% in decimal form) to find the interest earned.
3) The total interest earned on the entire investment of $9000 after one year can be represented by the algebraic expression:
Interest on ($×) + Interest on (9000 - $×)
To simplify this expression, combine like terms if possible, but since there are no like terms in this case, the expression remains as it is.
4) If you pay government tax on your interest at a rate of 33 cents in the dollar, the amount of money you receive from your interest after one year, after the tax is paid, can be represented by the algebraic expression:
Interest on ($×) + Interest on (9000 - $×) - (0.33) * [Interest on ($×) + Interest on (9000 - $×)]
To simplify this expression, distribute the -0.33 to each term inside the brackets, then combine like terms if possible.