Determine the amount of the ordinary annuities at the end of the given periods.
$200 deposited monthly at 1% per month for 20 months.
To determine the amount of the ordinary annuity at the end of the given periods, we can use the formula for the future value of an ordinary annuity:
FV = P × ((1 + r) ^ n - 1) / r
Where:
FV = Future Value
P = Periodic Payment
r = Interest Rate per period
n = Number of periods
In this case, the periodic payment (P) is $200, the interest rate (r) is 1% per month (or 0.01), and the number of periods (n) is 20 months.
Substituting these values into the formula, we get:
FV = $200 × ((1 + 0.01) ^ 20 - 1) / 0.01
Now, let's solve this equation step by step:
1. Calculate the interest rate plus 1: (1 + 0.01) = 1.01
2. Raise this value to the power of the number of periods: 1.01 ^ 20 ≈ 1.219924
3. Subtract 1 from the result: 1.219924 - 1 = 0.219924
4. Divide the result by the interest rate: 0.219924 / 0.01 = 21.9924
Finally, multiply this value by the periodic payment:
FV = $200 × 21.9924 ≈ $4,398.48
Therefore, the amount of the ordinary annuity at the end of the 20-month period is approximately $4,398.48.
What is
200( 1.01^20 - 1)/.01 ?
(I just plugged into the formula)