First Nation Bank is offering a two-year CD with 4.9% simple interest.
Second National Bank is offering a two-year CD with 4.8% compound interest (compound yearly).
Hint:
Variables stand for:
I = interest accumulated
T = time
R = the actual interest rate
- I = P * R * T (Simple interest)
- Y = A (1 + R)^n (Compound interest)
- ~ Y= ending value, A = Starting Amount, R = Interest Rate, N = the number of time periods / The amount of interest can be determined by subtracting the starting principal amount from the ending principal amount.
- Do they students need to hold another fund-raiser?
- How much will the class have in two years if it buys a First National Bank CD?
- How much will the class have in two years if it buys a Second National Bank CD?
- Which CD is the better deal? Explain your thinking. Did your calculations surprise you?
Bonus:
Assume next year’s 6th graders need $600 for its service project. If it can buy a two-year CD with a compound interest rate of 5%, how much does it need to raise at its fund-raiser?
A.L.
ReplyDeleteThe students do not need to hold another fundraiser since if they take the two year CD with First Nation Bank they’ll have $1,490 and with Second National Bank they’ll have $16,820. The better option for them to choose would be Second National Bank since you have 11 times the amount of money at the end of 2 years than you would have at the end of 2 years at First Nation Bank. My calculations surprised me because I was not thinking they would end up with $16,820 only at the end of 2 years. I was thinking at the most they would have around $2,000, $3,000.
HW
ReplyDeleteFirst National Bank total amount: $549 , I = 500 x .049 x 2.
Second National Bank total amount: $549.15 , Y = 500(1+.048)^2.
1. As long as the students go with one of the two banks, they will have enough money to build their flower beds after two years. If they go with First National Bank, they will have $4 left over. If they go with Second National Bank, there would be $4.15 left over.
2. In two years with First Nation Bank, the students will have $549.
3. In two years with Second National Bank, the students will have $549.15.
4. For the student’s situation, Second National Bank is a better deal since you collect 15 cents more than the other bank. My calculations did not surprise me, because since Second National Bank offers compound interest with an interest rate of 4.9%, which means they multiply 4.8% to the total amount after every year, while Second National Bank offers simple interest with an interest rate 4.9%, which means they take the amount they began with and multiply it by 4.9% after every year, and since compound interest has a higher total amount being multiplied after every year, I figured they would make more money, even in this case where is was only 15 cents more.
Bonus:
Equation : 600 - (500 x .05 x 2) = 50
They need to raise $50 at their fundraiser.
J.M.
ReplyDelete1) The students do not need to hold another fundraiser.
2) The students will have $49.00 at the end of the two year period.
3) The students will have $49.15 at the end of the two year period.
4) You would choose the compound interest it would give you $49.15 in the two years. With the simple interest you would get $49.00 in the two years. So I would go for the compound just for the extra 15 cents. Yes my calculations did surprise me. I thought that there would be a bigger difference.
MJS
ReplyDelete1.don’t need another fundraiser.
2.it will hold at the end of two years $49.
3. it will hold $49.15 in two years.
You would want to choose the compound interest. The compound interest gives you 15 cents more in the two years. With the simple interest you get $49 at the end of the two years. With the compound interest you’ll get $49.15 at the end of the two years.
AM
ReplyDeleteFirst Nation Bank’s total amount $549. I=500x0.049x2
Second Nation Bank’s total amount $549.15 I=500(1+.048) ^2
1. No the students do not need to have another fund raiser because no matter what bank they use they will have more then they need.
2. If they use First Nation Bank they will have $549. They will have $4 left over.
3. If they use Second Nation Bank they will have $549.15 which is $4.15 left.
4. I think the Second Nation Bank is better because you get more money and you have the same amount of years. No my calculations didn’t surprise me.
TM
ReplyDelete1. If the school puts there 500$ in either one they won’t have to have another fund raiser. For the first bank the equation would be i=500x4.8x2. There total amount would be 549$. The interest accumulated would be 49$. Since they only needed 545$, they would still have 4$ left over. For the other bank the equation is Y=500(1+4.8)^2. This would come to a total amount of 549.15$
2. If the class buys a CD from First National Bank they would have 549$ total after two years. I=500x4.8x2 =549$
3. If the class buys a CD from Second national Bank they would have a total of 549.15$ after two years. Y=500(1+4.8)^2
4. If you bought a two year CD, Second National Bank is a better deal. Using the equation to get the total for this bank, Y=500(1+4.8)^2, you would end up with a total of 549.15$. For First National Bank, I=500x4.8x2, you would end up with a total of 549$, an interest earned of 49$. With the Second bank you would gain an extra amount of .15$
Bonus:
The equation to find the new need is 600-(500x.05)^2=50
This signifies they would need to raise an extra 50$ for there new need of money.
A.L.
ReplyDeleteThe students do not need to hold another fundraiser since if they take the two year CD with First Nation Bank they’ll have $4,900 and with Second National Bank they’ll have $16,820. The better option for them to choose would be Second National Bank since you have about 3 times the amount of money at the end of 2 years than you would have at the end of 2 years at First Nation Bank. My calculations surprised me because I was not thinking they would end up with $16,820 or $4,900 only at the end of 2 years for both banks. I was thinking at the most they would have for both bank would be somewhere around $2,000 or $3,000.
LG
ReplyDelete1. they would have to do some more years if they chose the bank because I looked up the simple interest calculator and they only got an extra 24.50$ and the compound interest is 24$. So both of them need more then an extra year.
2. at the first national bank after 2 years it will be an extra 49 dollars making it 549.00$ making it enough to buy it.
3. at the second national bank after 2 years it would actually be an extra 49.15 dollars making it 549.15$ making it enough to buy it.
4. I would chose the second because it is an extra 15 cents just making the deal better then the first bank. My calculations surprised me because I expected I thought the first bank would be higher then the second.
AR
ReplyDeleteFirst National Bank: $549, Y=500x.049x2
Second National Bank: $549.15, Y=500(1+.048)^2
1. No matter what savings option the school chooses, they will not need to do another fundraiser. The only thing they need to make sure is that they use one of the two given savings options. They will make at least $4 more than they need.
2. In two years with First National Bank they will have $549.
3. In two years with Second National Bank they will have $549.15.
4. The better deal if your getting a two year CD is Second National Bank. The reason Second National Bank is better is because it makes you more money. Though $.15 isn’t very much money, it is still more. My calculations didn’t surprise me because I really didn’t know what to expect from Second National Bank in the first place.
Bonus
At the fundraiser they need to make at least $545 to have enough money.
AWM
ReplyDelete1. Yes, the students need the fundraiser if they want to raise the money for the flower beds.
2. If they bought the First National Bank CD they would have $9.8 at the end of two years.
3. If they bought the Second National Bank CD they would have $33.64 at the end of two years.
4. The Second National Bank CD would be a better deal. It would make a better deal because you would make more money at the end of two years. Yes, my calculations did not surprise me. The calculations that surprised me were the compound interest with the Second National Bank CD.
TD
ReplyDeletePlan one would get the students 549
Plan two would get the students 549.15
The students do not need to hold another fund raiser. Their total amount for either plan will be enough. However the compound interest plan would get them an extra 15 cents
.
The students would have 549.00 dollars after the two years with the simple interest plan.
The students would have 549.15 dollars after the two years with the compound interest plan.
The second national bank would be the better choice. The students would have an extra 15 cents. These calculations did surprise me because I thought the first national bank would be the better choice because its interest was higher but not compound.
BONUS
Next years Students would have to earn 550 dollars at their fundraiser in order to have enough money for their service project.
A.W
ReplyDeleteThe students don’t need to hold another fundraiser if they go with the Second National bank, but if they were to go with the First Nation Bank. That is because for the Second National bank the equation filled in would be 500(1+4.8) ^2. Then this would equal 16,820 dollars. The First Nation Bank’s equation is 500*4.9*2. This would equal 12,025 dollars. So if the students buy the First Nation Bank CD they will have 12,025 dollars, and if they buy the Second National Bank’s CD they would have 16,820 dollars. The second National Bank’s CD is a better deal. This result really surprised me. I though the bigger numbers would result in a bigger amount of money.
JD
ReplyDelete1. The student's money that they raised exceeds the amount in both plans so they do not need to do the fundraiser again
2. In the first nation bank's plan they would have an extra 49 dollars to the money earned in the fund raiser
3. In the second nation bank's plan they would have an extra 49.15 dollars added to the money in the fund raiser
4. Second nation banks deal is better because it has 15 cents more than first nations deal. This did not surprise me because it had an addition to the rest or the problem making it more than the problem before.
SK
ReplyDelete1) Using either interest plan, the students do not need to hold another fundraiser. When you calculate the interest of $500.00 with each interest plan, the results are $549.00 and $549.15. The cost of the project is $545.00, thus the students have enough money, with a few dollars to spare.
2) With the first national bank interest plan, the students will end up with $549.00.
3) With the second national bank interest plan, the students will end up with $549.15
4) The second national bank plan seems more efficient in my opinion. While the other plan gives you interest based on the original deposit, you gain interest on the interest with the second national bank. This will make the interest you gain increase, even though the interest rate is slightly smaller.
WO
ReplyDelete1) When using either one of the interest plans, the students do not need to hold another fundraiser. When the interest is $500.00 with both interest plans, the results are $549.00 and $549.15. The final price of the project is $545.00 and the students have enough money with some to spare.
2) With the first national bank interest plan, the students will have $549.00.
3) With the other national bank interest plan, the students will have $549.00.
4) The other national bank has a better deal. The other plan gives you interest based on the deposit while the second bank gives you interest based on the original deposit as well as interest previously earned. Even though the interest rate is smaller for the second bank, you end up with more money.
AWM
ReplyDelete1. Yes, the students need the fundraiser if they want to raise the money for the flower beds.
2. If they bought the First National Bank CD they would have $9.80 at the end of two years.
3. If they bought the Second National Bank CD they would have $33.64 at the end of two years.
4. The Second National Bank CD would be a better deal. It would make a better deal because you would make more money at the end of two years. Yes, my calculations did not surprise me. The calculations that surprised me were the compound interest with the Second National Bank CD.
RT
ReplyDelete1) The students do not need to have another fundraiser. When the interest is $500.00 with the two interest plans, the results are $549.15. The last cost of the project is $545.00 and the students have enough money to spare.
2) With the first national bank interest plan, the students will have $549.00.
3) With the second bank interest plan, the students will have $549.00.
4) The other national bank plan had the best deal. The other plan gives you interest based on the deposit, and the second bank gives you interest based on the original deposit as well as interest previously earned. Even though the interest rate is smaller for the second bank, you end up with more money.
AWM
ReplyDelete1. Yes, the students need the fundraiser if they want to raise the money for the flower beds.
2. If they bought the First National Bank CD they would have $509.80 at the end of two years.
3. If they bought the Second National Bank CD they would have $533.64 at the end of two years.
4. The Second National Bank CD would be a better deal. It would be a better deal because you would make more money at the end of two years. Yes, my calculations did surprise me. The calculations that surprised me were the compound interest with the Second National Bank CD.
MB
ReplyDelete1.) 1.The students will need to do another fund raiser.
2.) 2.If the students went with the First Nation Bank for a CD they would have $509.80 at the end of two years.
3.) 3.If the students went with the Second National bank for a CD then they would have $533.64 at the end of two years.
4.) 4.The second national bank CD would be the best deal. IT would earn more money by the end of two years. This does surprise me because the second national bank has a lower interest late.
E.R.
ReplyDelete1. The students don’t need to have another bake sale because they will have enough money through interest from their account.
2. 500*4.9*2=4900 First National Bank CD would give them $4900.
3. 500(1+4.8)^2=16820 Second National Bank would give them $16820.
4. They should go with Second National Bank. This is because they will have enough money to plant the flower beds and can give the extra money to either the senior center, the school, or the incoming 6th graders. I was shocked with the caculations because i thought they would not be as much.
MF:
ReplyDelete1.The students of 6th grade do not need to hold another bake sale because with the interest they get from their account, they will have enough money.
2.The First National Bank CD would have $4, 900. Equation: 500*4.9*2 = 4900.
3.The Second National Bank CD would have $16, 820. Equation: 500(1+4.8) = 16820.
4.I think that the 6th grade students should go with the Second National Bank CD because then they would have $16, 820. With this money, they would be able to buy the flower garden for the town’s senior center. Plus, they would have $16, 275 left over. They would be able to donate this money to the school or to the next incoming 6th graded students for their community project. Also they could donate some of the money to the senior center.
M.M
ReplyDelete1. The students do not need to do another fun-raiser because they will have enough money through interest through they’re account.
2. If they went with the first national bank CD they will have 4900 dollars.
3. If the students went with the second national bank thing they will have 16825 dollars.
4. The second national bank CD is a better deal because they have 11925 more dollars than the first national bank over the point of two years. My calculations do surprise me because the second national bank has less interest than the first national bank, even if that interest is 0.001 less interest.
ALW. The students do not need to hold another fundraiser because if they by the CD from Second national bank, it has a compound interest rate rather than a simple intrest rate. The kids would make 16825$ with the money from second national bank and only make 4900$ with first national bank.
ReplyDelete2. first national bank= 4900$
3. Second national bank-16825$
4. the better deal would be to buy a CD form the second national bank because of the compound intrest rate they make more than triple the amount of money, and would not have to have another fund raiser.
M.N.V.
ReplyDelete1. Yes the students need the fund raiser if they want to raise money for the flower bed.
2. If they bought First National Bank C.D. would have $509.80 at the end of two years.
3. If they bought the Second National Bank C.D. they would have $533.64 at the end of two years.
4. The Second National Bank C.D. would be better deal because they would make more money. My calculations did surprise me.
C.D.
ReplyDelete1. Yes the students need the fund raiser if they want to raise money for the flower bed.
2. If they bought the first national bank C.D. would have $509.80 at the end of two years.
3.If they bought the second national bank C.D. they would have $533.64 at the end of two years.
4. The second national bank C.D. would be a better deal because they would make more money. My calculations did surprise me.
ZB
ReplyDelete1. The students do not need to do another fundraiser because the interest they earn from the CD would bring them to a higher amount of money than $545.
2. Using the equation I = P * R * T, I plugged in the numbers for the situation into the variables. The new equation would be I = 500 * .49 * 2. After figuring out the equation, I got an outcome of $490. This number would be the amount of interest that they earn over 2 years. Adding that to the starting amount, the class would have $990.
3. Using the equation Y = A (1 + R)^n, I put the numbers of the situation into the variable’s places. The new equation would be Y = 500 (1 + .48)^2. The outcome of this equation is 1,095. Adding the starting 500, the number would be 1,595.
4. Second National Bank is the better deal because they would give the students so much more money than with First National Bank, but they are putting it in for the same amount of time.
BT
ReplyDelete1. They do not need to hold another fund-raiser. Since the students received $500 already from the bank, and they have $490 from their simple interest, they have $940 and they just need $545.
2. The class would have $490 after 2 years if they buy a First National Bank CD.
3. The class would have $1095.2 after 2 years if they buy a Second National Bank CD.
4. The Second National Bank has a better deal. This is because you get $1095.2 after two years and the First National bank you get $490 after two years.. The calculations did surprise me because I thought the First National bank might get more after two years because it has an interest rate of 4.9% and the Second National Bank has an interest rate of 4.8%.
E.E.W.
ReplyDelete1. The students do not need to hold another fundraiser. Since they already received $500 from their bake sale, and now they have another $490 from the interest, they have $990 in all. They only need $545, so they have a lot left over.
2. After two years, the class would have $490. This is because in 6th grade, they put in money, and in 8th grade (two years later) they have $490.
3. The class will have $1095 after two years. This is because you multiply the starting amount 1.48 by two. Then, you multiply that by 500.
4. The Second National bank has the better interest deal. This is because after two years, you end up with more money than with the First National bank. With the first bank, you have $490. With the second bank, you have $1095. This did surprise me because, the interest rate for the first bank is 4.9%, and the interest rate for the second bank is only 4.8%. Obviously, the first interest rate is a bigger number.
ZB
ReplyDelete1. The students do not need to do another fundraiser because the interest they earn from the CD would bring them to a higher amount of money than $545.
2. Using the equation I = P * R * T, I plugged in the numbers for the situation into the variables. The new equation would be I = 500 * .49 * 2. After figuring out the equation, I got an outcome of $490. This number would be the amount of interest that they earn over 2 years. Adding that to the starting amount, the class would have $990.
3. Using the equation Y = A (1 + R)^n, I put the numbers of the situation into the variable’s places. The new equation would be Y = 500 (1 + .48)^2. The outcome of this equation is 1,095. Adding the starting 500, the number would be 1,595.
4. Second National Bank is the better deal because they would give the students so much more money than with First National Bank, but they are putting it in for the same amount of time. I was surprised by the results because the interest for the other bank was higher than the one that had more interest.
MW
ReplyDelete1. Addy and Trey would not need to hold another fundraiser because if they open a CD, they would have over enough money to build the flower beds.
2. Using the equation, I = P*R*T, I was able to figure out that after two years of having a CD at First National Bank, Addy and Trey would have $990. To figure this out I just plugged the numbers from the situation into the equation and got an outcome of 490. I then added that number to the money they already had, 500, and got 990.
3. Using the equation, Y = A (1+R) ^ N, I was able to figure out that after two years of having a CD at Second National Bank, Addy and Trey would have $1,595 To figure this out I just plugged the numbers from the situation into the equation and got an outcome of 1,095. I then added that number to the money they already had, 500, and got 1,595.
4. Second National Bank has the better deal. After having a CD for two years there Addy and Trey would have over $600 more than they would have at First National Bank. I was very surprised by the results of my calculations. I was surprised because of how much more interest they would receive from Second National Bank than from First National Bank.
C.S.
ReplyDelete1.) Do the students need to hold another fund-raiser? The 6th grade students that attend Madison #1 Middle School do not need to do another fund raiser because they got $549.15, which is $4.15 over the cost of the town bed, which is more than what they needed.
2.) How much will the class have in two years if it buys a First National Bank CD?Since the equation is I=500*.049*2 the class would get only $49 from the First National Bank, because the time period that they get is not with an exponent, to make the amount of money increase by as much.
3.) How much will the class have in two years if it buys a Second National Bank CD? By following the information that was given about the variables, I could easily plug in the variables that I was given from the story.Y=500*(1+.048)^2. The class would have $1095.20 from the Second National Bank CD, because the time variable just needed to be changed to two years.
4.) Which CD is the better deal? Explain your thinking. Did your calculations surprise you? Second National Bank CD, would have the better deal because the overall amount that Addy could withdraw would be $549.15. By following the equation of Y=500*(1+.048)^2 I could easily find that the Second National Bank CD is better because I would just have to change the time variable to two years instead of one. I was surprised because I thought that the place with the compound interest would add up to less money based on the less amount of interest which was 4.8%.
E.A.W.
ReplyDelete10/29/10
1. Do they students need to hold another fund-raiser?
If the class buys either National Bank CD, they will have enough money added to their $500 to build flower beds at the senior center at the price of $545. So, the class will not need to have another fundraiser, they will get enough money using a National Bank CD.
2.) How much will the class have in two years if it buys a First National Bank CD?
(Variables stand for:
I = interest accumulated
T = time
R = the actual interest rate
I = P * R * T (Simple interest)
Y = A (1 + R)^n (Compound interest)
~ Y= ending value, A = Starting Amount, R = Interest Rate, N = the number of time periods / the amount of interest can be determined by subtracting the starting principal amount from the ending principal amount.)
I = 500 * .049 * 2 would be the equation for this problem. I found this equation by plugging in the starting amount of $500, the interest rate of 4.9% or 0.049, and the time of 2 years into the simple interest equation form. When computed, the equation tells me that in two years the class will have $49 if they buy a First National Bank CD.
3.) How much will the class have in two years if it buys a Second National Bank CD?
(Variables stand for:
I = interest accumulated
T = time
R = the actual interest rate
I = P * R * T (Simple interest)
Y = A (1 + R)^n (Compound interest)
~ Y= ending value, A = Starting Amount, R = Interest Rate, N = the number of time periods / the amount of interest can be determined by subtracting the starting principal amount from the ending principal amount.)
Y= 500 * (1+ .048)^2 would be the equation for this problem. I found this equation by inserting the starting amount of $500, the interest rate of 4.8% or 0.048, and the time of 2 years into the compound interest equation form. When calculated, the equation tells me that in two years the class will have $549.15 if they buy a Second National Bank CD.
4.) Which CD is the better deal? Explain your thinking. Did your calculations surprise you?
The school would get $549.15 if they use the Second National Bank’s CD compared to the First National Bank’s CD amount of $49. So, using the Second National Bank’s CD would be a better deal. This did not surprise me because although the Second National Bank had a lower interest rate than the other bank, part of it’s equation involved the exponent of 2. This meant that the first part of the equation’s answer would be multiplied by itself, which would create a much larger number than an equation with no exponents would.