Two investments earn a total annual income of $2825. One investment is in a 6.75% annual simple interest certificate of deposit. The other is in a 7.25% tax free annual simple interest account. The total amount invested is 40,000. Find the amount in invested in the certificate of deposit.
Well, it seems like these investments are earning a nice income. Let's solve this mystery!
Let's call the amount invested in the certificate of deposit "x" (let's hope x doesn't mark the spot). The amount invested in the tax-free account would then be 40,000 minus x.
Now, let's calculate the income from each investment. The income from the certificate of deposit, at 6.75%, would be x times 0.0675. The income from the tax-free account, at 7.25%, would be (40,000 - x) times 0.0725.
Since we know the total income is $2825, we can set up an equation:
0.0675x + 0.0725(40,000 - x) = 2825
Now, let's solve this equation and find out the amount invested in the certificate of deposit. Let the show begin!
0.0675x + 0.0725(40,000 - x) = 2825
0.0675x + 2900 - 0.0725x = 2825
-0.005x + 2900 = 2825
-0.005x = 2825 - 2900
-0.005x = -75
x = -75 / -0.005
x = 15,000
So, the amount invested in the certificate of deposit is $15,000. Now that's a nice chunk of change!
Let's assume the amount invested in the certificate of deposit is x dollars.
The amount invested in the tax-free account would then be (40,000 - x) dollars.
Using the formula for simple interest: Interest = Principal * Rate * Time,
The income from the certificate of deposit would be (x * 6.75%),
And the income from the tax-free account would be ((40,000 - x) * 7.25%).
According to the given information, the total annual income is $2825. So, we can write the equation:
(x * 6.75%) + ((40,000 - x) * 7.25%) = 2825
Simplifying the equation:
0.0675x + (0.0725)(40,000 - x) = 2825
28,500 - 0.0725x + 0.0675x = 2825
-0.005x = 2825 - 28,500
-0.005x = -25,675
Dividing both sides of the equation by -0.005:
x = (-25,675) / (-0.005)
x = 5,135,000
Therefore, the amount invested in the certificate of deposit is $5,135,000.
To solve this problem, let's represent the amount invested in the certificate of deposit as "x" (in dollars).
Given that the total amount invested is $40,000, we can infer that the amount invested in the tax-free account is (40,000 - x) dollars.
Now, let's calculate the annual income from each investment:
For the certificate of deposit, the annual income can be calculated using the formula:
Income = Principal * Rate
The rate of interest for the certificate of deposit is 6.75%, so the income from this investment would be:
Income1 = x * 6.75/100 = 0.0675x
Similarly, for the tax-free account, the income would be:
Income2 = (40,000 - x) * 7.25/100 = 0.0725(40,000 - x)
We know that the total annual income from both investments is $2825:
Income1 + Income2 = 2825
0.0675x + 0.0725(40,000 - x) = 2825
Now, let's solve this equation to find the value of x, representing the amount invested in the certificate of deposit.