Caroline is opening a CD to save for college. She is considering a 3-year CD or a year CD since she starts college around that time. She needs to be able to have the money to make tuition payments on time, and she does not want to have to withdraw money early from the CD and face a penalty. She has $19,400 to deposit.
a. How much interest would she earn at 4.2% compounded monthly for three years? Round to the nearest cent.
b. How much interest would she earn at 4.2% compounded monthly for years? Round to the nearest cent.
c. Caroline decides on a college after opening the year CD, and the college needs the first tuition payment a month before the CD matures. Caroline must withdraw money from the CD early, after 3 years and 5 months. She faces two penalties. First, the interest rate for the last five months of the CD was lowered to 2%. Additionally, there was a $250 penalty. Find the interest on the last five months of the CD. Round to the nearest cent.
d. Find the total interest on the year CD after 3 years and 5 months.
e. The interest is reduced by subtracting the $250 penalty. What does the account earn for the 3 years and 5 months?
f. Find the balance on the CD after she withdraws $12,000 after 3 years and five months.
g. The final month of the CD receives 2% interest. What is the final month’s interest? Round to the nearest cent.
h. What is the total interest for the year CD?
i. Would Caroline have been better off with the 3-year CD? Explain?

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?