after completing his CFP, andre was excited about the prospects of working in retirement planning. If an individual put the equivalent of $50 per month, or $600annually into an ordinary annuity, how much money would accumulate in 20 years at 3% compounded annually?
To calculate the amount of money that would accumulate in 20 years at 3% compounded annually, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
where:
FV = future value (amount of money accumulated)
P = periodic payment (amount contributed per period)
r = interest rate per period
n = number of periods
In this case, the periodic payment is $50 per month, or $600 annually. The interest rate is 3% per year (or 0.03), and there is a total of 20 years.
So, plugging these values into the formula:
FV = $600 * [(1 + 0.03)^20 - 1] / 0.03
To simplify the calculation, let's break it down step by step:
1. Calculate the value inside the parentheses:
(1 + 0.03)^20 = 1.03^20 ≈ 1.8061119
2. Calculate the numerator:
$600 * (1.8061119 - 1) = $600 * 0.8061119 ≈ $483.67
3. Calculate the denominator:
0.03
4. Divide the numerator by the denominator:
$483.67 / 0.03 ≈ $16,121.67
Therefore, after 20 years at 3% compounded annually, approximately $16,121.67 would accumulate in the ordinary annuity.