For 1 & 3, Simple Interest equals Principal times Interest rate times time (I = Prt). One of the things to remember (and often not discussed in textbooks) is that interest rates are percentages per unit time, e.g. 10% interest per year; 1.5% interest per
month. So if you have $100 at 10% interest (.1) per year, in the bank for a year, the simple interest is $10 [$10 = ($100) * (.1/yr.) * (1 yr.)]. But if you keep the $100 in the bank for only 6 months, the simple interest is only $5 [$5 = ($100) * (.1/yr.)
* (1/2 yr.)] For #1, you have to adjust rate to account for the time the money was in the account. For #3, you are given the interest, principal, and time, and asked to compute the rate, so r = I/Pt
For #2, In simple interest, the formula only accounts for the interest owed, and so the principal remains outstanding. So in the $100 @ 10% for 1 year example, there would be $110 in the bank account $100 in principal and $10 in interest, i.e. the amount
in the account is P + I where I = Prt.
For 4 & 5, your text should have examples of how to calculate these situations. The issue is how to address the partial payments of principal over time. For example, in #5, One way to calculate this using "simple interest" is to note that Carrie has paid
4 * 12 * $140 = $6720. She has to pay the $6000 in principal, and so pays $720 in interest. Using r = I/Pt, will give a simple interest rate.
There are more complicated methods to address the fact that of her $140/mo. payment is only $15 in interest and $125 principal, and so the amount of principal owed should be reduced over time, but usually this is addressed as part of compound interest.
If there are models in your text addressing this situation, you should use those instead of the one above, especially for #4.
If you have an example from your text, I would be happy to walk you through it, and I hope this helps. John