Find the future value of an annuity if you invest $200 quarterly for 20 years at 5% interest compounded quarterly.
To find the future value of an annuity, you can use the formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Payment per period
r = Interest rate per period
n = Number of periods
In this case, the payment per period (P) is $200, the interest rate per period (r) is 5% or 0.05, and the number of periods (n) is 20 years * 4 quarters per year = 80 quarters.
Let's substitute these values into the formula:
FV = $200 * ((1 + 0.05)^80 - 1) / 0.05
Now, let's calculate it step-by-step:
1. Calculate the numerator:
Numerator = (1 + 0.05)^80 - 1 ≈ 13.53064778
2. Calculate the denominator:
Denominator = 0.05
3. Divide the numerator by the denominator:
FV = $200 * (13.53064778 / 0.05)
4. Calculate the final result:
FV ≈ $54,122.59
So, the future value of an annuity, if you invest $200 quarterly for 20 years at 5% interest compounded quarterly, is approximately $54,122.59.
To find the future value of an annuity, you can use the formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity
P is the periodic payment (in this case, $200)
r is the interest rate per compounding period (in this case, 5% or 0.05)
n is the number of compounding periods (in this case, 20 years)
Let's break down the calculation step-by-step:
Step 1: Convert the annual interest rate to a quarterly interest rate:
Since the interest is compounded quarterly and the annual interest rate is 5%, we need to convert it to a quarterly interest rate by dividing it by 4:
Quarterly interest rate = 5% / 4 = 0.0125 (or 1.25%)
Step 2: Convert the number of years to the number of compounding periods:
Since the interest is compounded quarterly, we need to multiply the number of years by 4:
Number of compounding periods = 20 years * 4 = 80 quarters
Step 3: Plug the values into the formula and calculate:
FV = $200 * [(1 + 0.0125)^80 - 1] / 0.0125
After calculating this expression, the future value of the annuity will be obtained.