Find the amount of the annuity if the deposit is $800 quarterly for 6 years at 9% compounded quarterly.
Amount=?
To find the amount of the annuity, we can use the formula for the future value of an ordinary annuity:
A = P * [(1 + r/q)^(n*q) - 1] / (r/q)
Where:
A = Amount
P = Deposit amount
r = Annual interest rate (convert to decimal form)
q = Number of compounding periods per year
n = Number of years
In this case, the deposit amount (P) is $800, the annual interest rate (r) is 9% (or 0.09), the compounding periods per year (q) are 4 (since it's compounded quarterly), and the number of years (n) is 6.
Plugging in these values into the formula:
A = 800 * [(1 + 0.09/4)^(6*4) - 1] / (0.09/4)
Simplifying the equation:
A = 800 * (1.0225^(24) - 1) / (0.0225)
Using a calculator, calculate 1.0225^(24) and then multiply it by 800. Afterward, divide the result by 0.0225 to find the final amount (A).