when $70 is invested monthly with an annual compound interest rate of 12% interest compounded monthly what is the total amount of investment at the end of the second month
To find the total amount of 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.
First, let's calculate the compound interest for the first month.
The formula to calculate compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount, which is $70 in this case
r = annual interest rate (as a decimal), which is 12% or 0.12
n = number of times that interest is compounded per year, which is 12 (since it is compounded monthly)
t = the number of years, which is 1/12 (since it is 1 month)
Plugging in these values, we have:
A = 70(1 + 0.12/12)^(12*1/12)
A = 70(1.01)^1
A = 70(1.01)
A = 70.7
So, at the end of the first month, the investment amount is $70.70.
Now, let's calculate the compound interest for the second month.
Using the same formula again:
A = P(1 + r/n)^(nt)
Plugging in the new values, we have:
A = 70.7(1 + 0.12/12)^(12*1/12)
A = 70.7(1.01)^1
A = 70.7(1.01)
A = 71.407
So, at the end of the second month, the total amount of investment will be approximately $71.41.