Bernie has $16000 invested, part at 3% and the remainder at 5%. If the yearly interest on each investment is the same, how much interest does he receive each year?

Question

Bernie has $16000 invested, part at 3% and the remainder at 5%. If the yearly interest on each investment is the same, how much interest does he receive each year?

Answer 1

Let n and 16000-n be the amounts invested at 5% and 3%, respectively. Then:

.05(n)=.03(16000-n)
.08n=480
n=6000
.05n=300
.03(16000-n)=300
Both investments earn $300 apiece, making a grand total of $600 for the year. ☺☺☺☺

Answer 2

Let's denote the amount invested at 3% as x and the amount invested at 5% as y. We know that x + y = $16000.

Now, we need to set up an equation to find the interest earned from each investment each year. The formula to calculate interest is I = P * R * T, where I is the interest earned, P is the principal amount invested, R is the interest rate, and T is the time in years.

For the investment at 3%, the interest earned is:

I₁ = x * 0.03 * 1 (let's assume the time is 1 year)

For the investment at 5%, the interest earned is:

I₂ = y * 0.05 * 1

Since it is given that the yearly interest on each investment is the same, we can set up the following equation:

I₁ = I₂

x * 0.03 * 1 = y * 0.05 * 1

Simplifying the equation:

0.03x = 0.05y

Dividing both sides of the equation by 0.05:

0.03x/0.05 = 0.05y/0.05

0.6x = y

Now, we can substitute the value of y in terms of x back into the initial equation:

x + 0.6x = $16000

1.6x = $16000

Dividing both sides by 1.6:

x = $10000

Now, we can find the value of y:

y = 0.6 * $10000 = $6000

So, Bernie has invested $10000 at 3% and $6000 at 5%.

To calculate the interest received each year, we can use the interest formula again:

Interest from the investment at 3%:

I₁ = $10000 * 0.03 * 1 = $300

Interest from the investment at 5%:

I₂ = $6000 * 0.05 * 1 = $300

Therefore, Bernie receives $300 interest each year from both investments.

Answer 3

To find out how much interest Bernie receives each year, we need to calculate the interest earned on both investments separately.

Let's assume Bernie invested x dollars at 3%, and the remaining (16000 - x) dollars at 5%.

The formula to calculate simple interest is:

Interest = Principal * Rate * Time

For the first investment at 3%, the interest earned would be:

Interest₁ = x * 0.03

For the second investment at 5%, the interest earned would be:

Interest₂ = (16000 - x) * 0.05

We are given that the yearly interest on both investments is the same, so we can equate the interest:

Interest₁ = Interest₂

x * 0.03 = (16000 - x) * 0.05

Now we can solve this equation to find the value of x.