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:
\(P = \frac{A}{(1+r)^n}\)
Where:
P = principal amount at the beginning
A = amount at the end of the preceding period
r = interest rate per period
n = number of periods
In this case, since the investment is made monthly, the interest rate per period is the annual interest rate divided by 12 (compounded monthly).
Let's break down the calculation step by step:
1. Calculate the amount at the end of the first month:
\(A = 120 \times (1 + \frac{0.06}{12})^1\)
2. Substitute the value of A into the formula to find the principal amount at the beginning of the second month:
\(P = \frac{120 \times (1 + \frac{0.06}{12})^1}{(1 + \frac{0.06}{12})^1}\)
Simplifying the equation further:
\(P = 120 \times (1 + \frac{0.06}{12})^1\)
Therefore, the calculation that explains how to find the principal amount at the beginning of the second month is:
\(P = 120 \times (1 + \frac{0.06}{12})^1\)
What
The calculation that explains how to find the principal amount at the beginning of the second month is:
\(P = 120 \times (1 + \frac{0.06}{12})\)
I can’t read the answer
Apologies for the formatting issue. The calculation that explains how to find the principal amount at the beginning of the second month is:
\(P = 120 \times (1 + \frac{0.06}{12})\)
No
I apologize for the confusion. Let me provide a simpler and clearer calculation:
To find the principal amount at the beginning of the second month, you can subtract the interest earned in the first month from the total amount invested.
1. Calculate the interest earned in the first month:
Interest = Total amount invested × (Monthly interest rate)
Interest = $120 × (0.06/12)
2. Subtract the interest earned from the total amount invested to find the principal amount at the beginning of the second month:
Principal at the beginning of the second month = Total amount invested - Interest earned
Therefore, the calculation to find the principal amount at the beginning of the second month is:
\(Principal = $120 - [($120 × 0.06)/12]\)