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.
What is the total amount of the investment at the end of the second month?
To find the total amount of the investment at the end of the second month, we need to calculate the compound interest for two months.
First, we need to calculate the monthly interest rate. Since the annual interest rate is 12%, the monthly interest rate is 12%/12 = 1% = 0.01.
Next, we can use the formula for compound interest:
A = P(1+r/n)^(nt)
where A is the final amount, P is the principal (the amount invested monthly), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $70, r = 0.12, n = 12 (compounded monthly), and t = 2/12 (two months).
A = $70(1+0.12/12)^(12*2/12)
A = $70(1+0.01)^(2)
A = $70(1.01)^(2)
A = $70(1.0201)
A ≈ $70.40
Therefore, the total amount of the investment at the end of the second month is approximately $70.40.