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.(1
To find the total amount of the investment at the end of the second month, we need to calculate the compound interest for each month and add it to the principal.
The formula for compound interest is:
$P = A(1 + r/n)^(nt)
Where:
P = the future value of the investment/loan, including interest
A = the initial deposit or principal amount (in this case $70)
r = the annual interest rate (12%)
n = the number of times that interest is compounded per year (monthly = 12)
t = the number of years the money is invested for (2 months = 2/12 = 1/6 year)
Plugging in the values:
$P = 70(1 + 0.12/12)^(12 * 1/6)
= 70(1 + 0.01)^(2)
= 70(1.01)^(2)
= 70(1.0201)
= 70 * 1.0201
= 71.407
Rounding to two decimal places, the total amount of the investment at the end of the second month is $71.41.