Hi guys,

I'm trying to help my son with this question but I just have no idea how to set it up. I know that I=prt, but I don't understand what to plug in here since we are given two bonds.

Anita Ramirez owns two bonds, one paying 8.5% interest and the other paying 9% interest. Every six months Anita receives total of $485 interest from both bonds. If the 8.5% bond is worth $4000, how much is the 9% bond worth?

Thanks,
Samina

The semiannual interest paid on the 8.5% bond is 0.085 x 4000 x 1/2 = $170. (That factor of 1/2 is there because the payments are made twice a year.) That leaves $485 - $170 = $315 as the semiannual interest on the 9% bond. Solve for its principal, P, with the formula

0.09 x P x (1/2) = $315
P = 630/0.09 = $7000.

The last step required some algebraic manipulation that I hope you were able to follow.

what is the difference between the simple and compound semi annually interst on 250 dollars in 2 years at 14%

Hi Samina, I can help you with that!

To solve this problem, we can set up two equations - one for each bond.

Let's call the value of the 9% bond "x".

According to the problem, Anita receives a total of $485 in interest every six months from both bonds. The interest earned from the 8.5% bond is calculated using the formula I = prt, where "I" represents the interest, "p" represents the principal (or value of the bond), "r" represents the interest rate, and "t" represents the time (in this case, six months).

For the 8.5% bond, we know that the interest rate (r) is 8.5%, the principal (p) is $4000, and the interest (I) is unknown. Using the formula, we can set up the equation:

I1 = 0.085 * 4000

Now, for the 9% bond, we know that the interest rate (r) is 9%, the principal (p) is "x" (the value we are trying to find), and the interest (I) is also unknown. Setting up the equation:

I2 = 0.09 * x

Since Anita receives a total of $485 interest every six months, we can add the interest from both bonds and set it equal to $485:

I1 + I2 = 485

Now, we can substitute the values from the equations we set up:

0.085 * 4000 + 0.09 * x = 485

Simplifying the equation:

340 + 0.09x = 485

Now, we can solve for "x", the value of the 9% bond:

0.09x = 485 - 340

0.09x = 145

Divide both sides of the equation by 0.09:

x = 145 / 0.09

x ≈ 1611.11

Therefore, the 9% bond is worth approximately $1611.11.

I hope this helps! Let me know if you have any further questions.