A total of $12,000 is invested in two funds paying 9% and 11% simple interest. If the yearly interest is $1,180, how much of the $12,000 is invested at each rate?
We have two unknowns: the amount of money invested at 9% and the amount of money invested at 11%.
Sentence (1) ''A total of $12,000 is invested in two funds paying 9% and 11% simple interest.'' can be restated as (The amount of money invested at 9%) (The amount of money invested at 11%) $12,000.
Sentence (2) ''If the yearly interest is $1,180, how much of the $12,000 is invested at each rate?'' can be restated as (The amount of money invested at 9%) 9% + (The amount of money invested at 11% 11%) total interest of $1,180.
In shortcut form: (1) x+y=$12000 (2) .09x+.11y=$1180
Principal of P dollars = P dollars* Rate in decimal * time in years
Can you show me how you get interest 0.09x on aPrincipal of x dollars?
from your first equation
x + y = 12000 ---> y = 12000 - x
sub that into the other equation:
.09x + .11y = 1180
.09x+ .11(12000-x) = 1180
.09x+ 1320 - .11x = 1180
-.02x = -140
x = 7000
then y = 12000 - 7000 = 5000
$7000 was invested at 9%, and $5000 was invested at 11%
check:
.09(7000) + .11(5000)
= 630 + 550 = 1180
Suppose that $2000 is invested at a rate of 3.3% ,total amount after 3 years.
Sure, let me explain how we calculate the interest on a principal of x dollars at a rate of 9%.
The formula to calculate the interest is:
Interest = Principal * Rate * Time
In this case, the principal is x dollars and the rate is 9%, or 0.09 in decimal form. Let's assume the time is 1 year for simplicity.
Substituting these values into the formula, we have:
Interest = x * 0.09 * 1
Simplifying the expression, we get:
Interest = 0.09x
So, the interest on a principal of x dollars at a rate of 9% is 0.09x.
To find the interest on a principal amount of x dollars at a rate of 9%, you can use the formula:
Interest = Principal * Rate * Time
In this case, the rate is given as a decimal (0.09), and the time is one year. So, the interest on an amount of x dollars at a rate of 9% would be:
Interest = x * 0.09 * 1
Simplifying this expression gives:
Interest = 0.09x
Therefore, the expression 0.09x represents the interest on a principal amount of x dollars at a rate of 9%.
To calculate the interest earned on an investment, you multiply the principal (the amount of money invested) by the interest rate and the time period in years.
In this case, the interest earned on an investment of x dollars at an interest rate of 9% is calculated as follows:
Interest = Principal * Rate * Time
= x * 0.09 * 1
The time period is 1 year because it is specified as the "yearly interest" in the question.
Simplifying the equation, we have:
Interest = 0.09x
Therefore, the interest earned on an investment of x dollars at an interest rate of 9% is 0.09x.