Okay, We are here to help Caroline work through this complicated situation, starting with Part A. She's investing $19,400 for three years out of 4.2% interest rate, compounded monthly on because it's monthly and equals 12. So we're going to figure out the amount of interest you would earn. First, let's find the final balance using the equation. B equals P Times one plus R over in to the anti. Okay, well, substitute all of our values in their 19,400. And for our we're going to use 0.0 for two. We need to convert that percent to a decimal and for N. We're using 12 and we're raising it to the 12 times three, which is the 36th power. So let's see what we get for that. So the final balance there is $22,000 and 23 cents. Well, we want to know the interest, so we need to subtract the original principle from that amount to get the interest. So we're going to subtract 19,400 from that amount, and the interest is $2600.23 Okay. Now let's work on part B to figure out the amount of interest you would earn with the other CD. So the other CD is also compounded monthly. So in is still 12. Same interest rate, longer period of time. Okay, so we're substituting our numbers into the same formula and we have 19,400 times one plus 10.4 to over 12 raised to the 12 times 3.5, and we end up with $22,466 and 30 cents. Now that's the final balance, and we want to know the interest. So we're going to subtract the original $19,400 from that, and the interest would be $3066.30. Okay, now we're in part C, and some things have changed for Caroline, and now she's earning her 4.2% interest for the 1st 3 years. But then she's only earning 2% for the last five months, and we want to calculate the amount of interest she earns in those last five months. But we have to start by figuring out what she's starting with at the beginning of that time period. So we need to know how much money she had in her account at the end of three years. So let's use the formula B equals P 19,400 times one plus 0.4 to over 12 to the three times 12 to figure out how much she had in her account at the end of three years. And you know, that is exactly what we did for part a. Come to think of it, we got $22,000.23 so why not take advantage of that? Okay, so what's gonna happen then is for the last five months of the CD, she's going to be earning interest on that particular principle. So we're going to use that as our new value of P over here for the final part of the CD. So now we're going to have B equals $22,000.23 times one plus 10.2 because now she's only earning 2% divided by 12. And for how long? Well, she's doing this for five months, so that's 5/12 of a year times 12 times per year. So that's really just a next opponent of five. It's gonna be five compound ing's and let's calculate that amount. So the final mountain now final amount now is $22,184.18. Okay, so the question is, how much interest did she earn in those last five months? So we need to subtract from this amount the principal. So we need to take $22,184.18 and subtract $22,000.23 and we end up with $183.85. That's the amount of interest she earned in that last five month period. Now, in Part D, we want to know how much interest she earns altogether. So the 1st 3 years she earned $2600.23 and in the last five months she earned $183.85. Those were answers from Parts A and C, and if we add those together, we'll get the total interest. So over the 3.5 year period, she actually earned $2784.8 sense of interest. Now what happens in Part E is we have to subtract the penalty so she pays a $250 penalty for early withdrawal on her CD. So we're going to subtract this from the amount of interest. So we have $2784.8 sense of interest. We're going to subtract the $250. So the amount of interest she actually gets after subtracting the penalty is $2534.8. Okay, now, in part F, she's going to withdraw $12,000. And so let's figure out how much money shall have left. What will her balance be? So remember her principal was $19,400 and her interest minus for penalty, which we just found in the previous part was $2534 and eight cents. So altogether, the amount of money she has is $21,934.8. Now we need to subtract $12,000. She's going to withdraw that from for, uh, for school expenses and that leaves her with $9934.8. Okay, now we're on part G. Now. Three years and five months have gone by and remember that she has this CD for three years and six months. So there's still one more month to go, and she's going to make 2% interest during that month. So she's making 2% interest on her $9934.8 that remains in the CD. So let's figure out the balance. We would start with the principal $9934.8 and multiply it by one plus 10.0 to over 12 to the first, okay, just one month of interest. And that ends up giving us a balance of 9000 $950 and 64 cents. So that's the total. What amount of that is the interest we need to subtract the principal from that and we get the interest. So we take 9950 64 cents and subtract the principal 9934 and eight cents, and we end up with $16.56. That's the amount of interest she made during that final month. So for the next part, let's find her total interest for part for the entire 3.5 years. And this is part H. So remember, for the 1st 3 years, her interest waas $2600.23. Then for five months her interest waas $183 and 85 cents. Then, for the last month, her interest waas $16.56. So the total of those is $2800 and 64 cents. So the total interest she earned was that now that looks like it's better than the 3% or the three year CD, because the three year CD was $2600 of interest. This is $2800 of interest. But don't forget that she had to pay a $250 penalty. So the extra $200 an interest is wiped out by that $250 penalty, and she actually got last then $2600. If you think about it that way. So when all was said and done. If she had just invested in the three year CD, she wouldn't have had to pay the penalty and she would have been better off.