Eloise is investing and retirement account. She plans on adding an additional $50 at the end of every year and the expected monthly rate of return is 3% of the amount invested, calculated at the end of the month. If she starts with $1000 in the account find an equation that models the amount of money in the account each month for their first year.
A) y=50x+1000
B) y=1000(0.03)^x
C) y=1000(1.03)^x
D) y=50.03x+1000
This relationship is best modeled by an exponential function. Each month the amount is going up by 3% so the best function to model this situation is y = 1000(1.03)^x where 1000 is the initial rent and 1.03 represents that it increases by 3% each year. Since the $50 is only added at the end of each year it will not come into play in the monthly equation.
Therefore it would be C. y=1000(1.30)^x
To find an equation that models the amount of money in Eloise's account each month for the first year, we need to consider the starting amount, the additional amount she adds at the end of every year, and the monthly rate of return. Let's break it down step by step:
1. Starting with $1000: This is the initial amount in Eloise's account.
2. Adding $50 at the end of every year: Since she plans to add $50 at the end of every year, we need to account for this increase. However, the question specifies that this is a monthly calculation, so we need to convert this to a monthly value.
To calculate the monthly additional amount, we divide $50 by 12 (number of months in a year):
Additional Monthly Amount = $50 ÷ 12 = $4.17 (rounded to two decimal places)
3. Expected monthly rate of return: The question states that the expected monthly rate of return is 3% of the amount invested, calculated at the end of the month. This means that each month, Eloise's account grows by 3% of the previous month's balance.
To calculate the growth for each month, we multiply 3% (0.03) by the previous month's balance.
Now that we have the necessary information, let's create the equation that models the amount of money in the account each month for the first year:
Initial Amount: $1000
Additional Monthly Amount: $4.17
Monthly Rate of Return: 3% (0.03)
The equation that models the amount of money in the account each month for the first year would be:
y = (Initial Amount) + (Additional Monthly Amount * Month Number) + (Monthly Rate of Return * Previous Month's Balance)
Substituting the given values:
y = 1000 + 4.17x + 0.03 * Previous Month's Balance
Since we are calculating it for the first year, the Previous Month's Balance can be considered the Initial Amount, which is $1000.
Therefore, the correct equation that models the amount of money in the account each month for the first year is:
y = 1000 + 4.17x + 0.03 * 1000
Simplifying:
y = 1000 + 4.17x + 30
This can be further simplified to:
y = 1030 + 4.17x
So, the correct answer is D) y = 50.03x + 1000.
post it.
Who is making up your questions. Your answers contain x's and y's, but no x and y appears in your stated problem, nor do you define x and y
choices B and C are the same
The $50 at the end of the year have nothing to do with the problem, you only want the amount for the first year.
now: 1000
end of 1 month : 1000(1.03)^1
end of 2 months: 1000(1.03)^2
end of 3 months : 1000(1.03)^3
....
what do you think?