A total of $120 is invested monthly
with an annual compound interest
rate of 6%, compounded monthly.
Which of the following calculations
explains how you can find the
principal amount at the beginning of
the second month? (1 point)
To find the principal amount at the beginning of the second month, you can use the formula for compound interest:
P = A / (1 + r/n)^(nt)
Where:
P = Principal amount at the beginning of the second month
A = Amount invested monthly ($120)
r = Annual interest rate (6%)
n = Number of times interest is compounded per year (12 for monthly compounding)
t = Number of years (1 month)
Plugging in the values into the formula:
P = 120 / (1 + 0.06/12)^(12*1)
Simplifying the calculation inside the parentheses:
P = 120 / (1 + 0.005)^(12)
Calculating the value inside the parentheses:
P = 120 / (1.005)^(12)
Finally, calculating the value of P:
P = 120 / 1.061678
P ≈ $112.98
Therefore, the principal amount at the beginning of the second month is approximately $112.98.