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.
wrong
To solve this problem, we can use the formula for the future value of an investment with compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (in this case, the monthly deposit of $70)
r = the annual interest rate (12% or 0.12)
n = the number of times that interest is compounded per year (monthly, so n = 12)
t = the number of years (or in this case, the number of months, so t = 2)
Plugging in the values:
A = 70(1 + 0.12/12)^(12*2)
Simplifying the exponent:
A = 70(1 + 0.01)^(24)
Calculating the exponent:
A = 70(1.01^24)
Using a calculator, we find:
A ≈ 70(1.270096) ≈ 89.00672
Rounding to two decimal places, the total amount of the investment at the end of the second month is approximately $89.01.
I apologize for the mistake. Let's solve the problem correctly.
To calculate the total amount of the investment at the end of the second month, we need to find the future value of each monthly deposit and add them together.
First, let's calculate the future value of the first monthly deposit of $70 after one month:
A1 = P(1 + r/n)^(nt)
A1 = $70(1 + 0.12/12)^(12*1)
A1 = $70(1 + 0.01)^12
A1 = $70(1.01)^12
A1 ≈ $70(1.126825) ≈ $79.78
Now, let's calculate the future value of the second monthly deposit of $70 after two months:
A2 = P(1 + r/n)^(nt)
A2 = $70(1 + 0.12/12)^(12*2)
A2 = $70(1 + 0.01)^24
A2 ≈ $70(1.01)^24
A2 ≈ $70(1.270096) ≈ $88.91
Finally, we add the two future values together to find the total amount of the investment at the end of the second month:
Total amount = A1 + A2
Total amount ≈ $79.78 + $88.91
Total amount ≈ $168.69
Therefore, the total amount of the investment at the end of the second month is approximately $168.69 rounded to two decimal places.