When $70 is invested monthly with an annual compound interest rate of 12% interest, compounded monthly, what is the total amount of the investment at the end of the second month? Round the answer to two decimal places as needed.(1 point)
The total amount of the investment at the end of the second month is $__
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of the investment at the end of the second month
P = the monthly investment amount, which is $70
r = the annual interest rate, which is 12% or 0.12
n = the number of times the interest is compounded per year, which is 12 since it is compounded monthly
t = the time in years, which is 2/12 or 1/6 since it is two months out of a year
Plugging in the values, we get:
A = 70(1 + 0.12/12)^(12(1/6))
A = 70(1 + 0.01)^(2)
A = 70(1.01)^(2)
A = 70(1.0201)
A = 70.404
Rounding to two decimal places, the total amount of the investment at the end of the second month is $70.40.
wrong
I apologize for the confusion. Let's calculate the correct answer.
To find the total amount of the investment at the end of the second month, we need to calculate the compound interest for each month and add it to the initial investment.
The initial investment is $70.
First, we need to find the compound interest for the first month:
Interest for the first month = $70 * (0.12/12) = $0.70
So, at the end of the first month, the total amount is $70 + $0.70 = $70.70.
Now, we need to find the compound interest for the second month:
Interest for the second month = $70.70 * (0.12/12) = $0.707
So, at the end of the second month, the total amount is $70.70 + $0.707 = $71.41.
Rounding to two decimal places, the total amount of the investment at the end of the second month is $71.41.
wrong again
I apologize for the continued errors. Let's try again.
To find the total amount of the investment at the end of the second month with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the total amount
P = the monthly investment amount = $70
r = the annual interest rate = 12% = 0.12
n = the number of times interest is compounded per year = 12
t = the time in years = 2/12 = 1/6
Plugging in the values, we get:
A = 70(1 + 0.12/12)^(12*1/6)
A = 70(1 + 0.01)^(2)
A = 70(1.01)^(2)
A = 70(1.0201)
A ≈ 71.41
Rounding to two decimal places, the total amount of the investment at the end of the second month is approximately $71.41.