Find the future value of an ordinary annuity. Payments are made and interest is compounded as follows:
R=600
7% interest compounded quarterly
for 5 years
I set this up as follows and still am getting the wrong answer:
500 (1.07)^5-1/0.07
Please help!!
It's compounded quarterly, not annually, so divide the interest rate by 4 and multiply the exponent by 4.
To find the future value of an ordinary annuity, you can use the formula:
FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)
Where:
FV = Future Value
P = Payment amount
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In your case, the payment amount is $600, the annual interest rate is 7% (or 0.07 as a decimal), and compounding is done quarterly (n=4) for a period of 5 years (t=5).
Using these values, let's calculate the future value step by step:
Step 1: Convert the annual interest rate to the quarterly interest rate:
Quarterly interest rate (r/n) = 0.07 / 4 = 0.0175
Step 2: Calculate the total number of compounding periods:
Total number of compounding periods (n*t) = 4 * 5 = 20
Step 3: Substitute the values into the formula and calculate:
FV = 600 * [(1 + 0.0175)^(20) - 1] / 0.0175
Let's calculate this on a calculator:
(1 + 0.0175)^(20) will give you the value of (1.3837).
Then, substitute the value into the formula:
FV = 600 * (1.3837 - 1) / 0.0175
Calculate (1.3837 - 1) = 0.3837.
Now, substitute the value:
FV = 600 * 0.3837 / 0.0175
Calculating 600 * 0.3837 = 230.22.
Now, substitute the value:
FV = 230.22 / 0.0175
Finally, calculate 230.22 / 0.0175 = 13,171.43.
Therefore, the future value of the ordinary annuity is approximately $13,171.43.