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.
The total amount of the investment at the end of the second month is $____.
To calculate the total amount of the investment at the end of the second month, we need to find the future value of the investment after two months using the compound interest formula.
The formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, the principal amount (P) is $70, the annual interest rate (r) is 12% or 0.12, the interest is compounded monthly (n = 12), and the number of years (t) is 2/12 (as it is the second month).
Substituting the given values into the formula:
A = 70(1 + 0.12/12)^(12*(2/12))
Simplifying:
A = 70(1 + 0.01)^(1)
A = 70(1.01)
A = $70.70
Therefore, the total amount of the investment at the end of the second month is $70.70.