A total of $120 is invested monthly with an annual compound interest rate of 6%compounded monthlyWhich of the following calculations explains how you can find the principal amount at the beginning of the second month? (point) 120-2 120(1 + 0.06) + 120; 120 * (1 + 0.005) ^ 2; 120(1 + 0.005) + 120
To find the principal amount at the beginning of the second month, you can use the formula:
Principal amount = Previous principal amount + Monthly investment
Therefore, the correct calculation would be:
120 + 120 = 240
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Apologies for the confusion. Let's go through the options provided.
Option 1: 120 - 2
This calculation does not involve any interest or compounding. It simply subtracts 2 from the total investment, which is not relevant to finding the principal amount at the beginning of the second month.
Option 2: 120(1 + 0.06) + 120
This calculation assumes that the monthly investment is added to the principal amount and then a compound interest of 6% is applied. However, the monthly investment should be added separately from the interest calculation.
Option 3: 120 * (1 + 0.005) ^ 2
This calculation correctly accounts for monthly compounding. It first adds 0.5% (0.005) to 1, representing the monthly interest rate. Then it raises this value to the power of 2, as we want to find the principal amount at the beginning of the second month. Finally, it multiplies the result by the initial investment of $120.
Option 4: 120(1 + 0.005) + 120
This calculation does not account for compounding on a monthly basis. It simply adds 0.5% (0.005) to 1, representing the monthly interest rate, and then multiplies the result by the initial investment of $120.
Therefore, the correct calculation to find the principal amount at the beginning of the second month is 120 * (1 + 0.005) ^ 2.
Use the table to answer the question Monthly Contribution Total Amount After 3 Years of Investment (dollars) with a 4.2% Annual Interest Rate (dollars ) 125 4,803.64 175 6,725.09 225 8,646.54 300 11,528.72 The information in the table shows how much a specific monthly contribution can result in after 3 years of investment with a 4.2% annual interest rate, compounded monthly On average, the annual cost to attend a 2-year public institution in the 2020-2021 academic year is $3,900. If the goal is to cover the cost for two years at a 2-year public institution after 3 years of investment, what is the minimum amount a student should be saving each month? ( 1 point)
To find the minimum amount a student should be saving each month to cover the cost for two years at a 2-year public institution after 3 years of investment, we need to consider the total amount after 3 years of investment for different monthly contributions.
Looking at the table, we can see that the total amount after 3 years of investment ranges from $4,803.64 to $11,528.72 depending on the monthly contribution. The goal is to cover the cost for two years at a 2-year public institution, which is $3,900 per year.
Therefore, the minimum amount a student should be saving each month should be equal to or greater than the cost of two years at a 2-year public institution divided by the total number of months (36) in 3 years.
Cost for 2 years = $3,900/year x 2 years = $7,800
Minimum monthly contribution = $7,800 / 36 months ≈ $216.67
So, the minimum amount a student should be saving each month is approximately $216.67.
The information in the table shows how much a specific monthly contribution can result in after 3 years of investment with a 4.2% annual interest rate , compounded monthly On average, the annual cost to attend a 2-year public institution in the 2020-2021 academic year is $3,900. If the goal is to cover the cost for two years at a 2-year public institution after 3 years of investment, what is the minimum amount a student should be saving each month? (1 point) $ 300 $175 $ 225 $125
To cover the cost for two years at a 2-year public institution after 3 years of investment, we need to find the monthly contribution in the table that results in a total amount equal to or greater than the cost.
Looking at the table, we see that the total amount after 3 years of investment ranges from $4,803.64 to $11,528.72 for different monthly contributions.
The annual cost to attend a 2-year public institution is $3,900. For two years, it would be $3,900 x 2 = $7,800.
The minimum amount a student should be saving each month should be equal to or greater than the cost for two years at a 2-year public institution divided by the total number of months in 3 years (36).
Therefore, the minimum amount a student should be saving each month would be at least $7,800 / 36 months ≈ $216.67.
None of the provided options ($300, $175, $225, $125) matches the calculated minimum amount.