Suppose that you were saving money over 5 years to use in a purchase later. You have $1000 to put in the savings. After surveying several banks for savings plans, you found these options. "A" stands for the amount you will have in the bank after x years.
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Option A: Your money would receive simple interest at the end of 5 years.
The formula is A = 1000 + 1000(0.05) x.
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Option B: Your money will be compounded continuously.
The formula is A = (1000)(2.71828)(0.05 x).
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Option C: You will invest in a CD (Certificate of Deposit) compounded yearly.
The formula is A = (1000)(1.05) x.
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Option D: Buy a US Savings Bond. Buy at $1000 now.
When cashed in 5 years later, the amount will be $1267.
Calculate each of these. You can find this by substituting x = 5 in each formula. Note that there is no formula in the US Savings Bonds option, just the amount.
Post a response with your answers to the following questions.
1. What is the order of Options A, B, C, and D, listing the option which gives the greatest amount at the end of 5 years to the least?
2. Which option gave you the greatest amount at the end of the five years?
3. What was the amount you calculated with this option?
I figured it out
1. BCDA
2. B gave the greatest amount
3. $1284
To calculate the amount for each option, we can substitute x = 5 into the given formulas.
Option A:
A = 1000 + 1000(0.05) x
A = 1000 + 1000(0.05)(5)
A = 1000 + 1000(0.25)
A = 1000 + 250
A = 1250
Option B:
A = (1000)(2.71828)(0.05 x)
A = (1000)(2.71828)(0.05)(5)
A = (1000)(2.71828)(0.25)
A ≈ 1339.66
Option C:
A = (1000)(1.05) x
A = (1000)(1.05)(5)
A = (1000)(1.05^5)
A ≈ 1276.28
Option D:
The amount is given as $1267.
Now let's answer the questions:
1. The order of Options A, B, C, and D from greatest amount at the end of 5 years to least is:
- Option B ($1339.66)
- Option C ($1276.28)
- Option D ($1267)
- Option A ($1250)
2. Option B gave the greatest amount at the end of five years.
3. The amount calculated with Option B is approximately $1339.66.