When 70 dollars is invested monthly with an annual compound interest rate of 12% 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
To calculate the total amount of the investment at the end of the second month, 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 initial principal amount (in this case, $70)
r = the annual interest rate (12% or 0.12 in decimal form)
n = the number of times that interest is compounded per year (monthly, so 12)
t = the number of years (2 months, so 2/12 or 1/6 in years)
Plugging in these values, we have:
A = 70(1 + 0.12/12)^(12*(1/6))
Simplifying,
A = 70(1 + 0.01)^(2)
A = 70(1.01)^2
A = 70(1.0201)
A ≈ $71.40
Therefore, the total amount of the investment at the end of the second month is approximately $71.40.
wrong
I apologize for the mistake. Let's recalculate:
To calculate the total amount of the investment at the end of the second month, 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 initial principal amount (in this case, $70)
r = the annual interest rate (12% or 0.12 in decimal form)
n = the number of times that interest is compounded per year (monthly, so 12)
t = the number of years (2 months, so 2/12 or 1/6 in years)
Plugging in these values, we have:
A = 70(1 + 0.12/12)^(12*(1/6))
Simplifying,
A = 70(1 + 0.01)^(2/6)
A = 70(1.01)^(1/3)
Using a calculator, we find that (1.01)^(1/3) is approximately 1.003333.
A ≈ 70 * 1.003333
A ≈ $70.23
Therefore, the total amount of the investment at the end of the second month is approximately $70.23.
that's wrong
Apologies for the mistake. Let's recalculate correctly:
To calculate the total amount of the investment at the end of the second month, 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 initial principal amount (in this case, $70)
r = the annual interest rate (12% or 0.12 in decimal form)
n = the number of times that interest is compounded per year (monthly, so 12)
t = the number of years (2 months, so 2/12 or 1/6 in years)
Plugging in these values, we have:
A = 70(1 + 0.12/12)^(12*(1/6))
Simplifying,
A = 70(1 + 0.01)^(2/12)
A = 70(1.01)^(1/6)
Using a calculator, we find that (1.01)^(1/6) is approximately 1.001667.
A ≈ 70 * 1.001667
A ≈ $70.12
Therefore, the total amount of the investment at the end of the second month is approximately $70.12.