If Don Gecewicz invests $5000 at 9% interest compounded quarterly, find the amount after 4 years.
$104,924
To find the amount after 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount after t years
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, Don Gecewicz invests $5000, the interest rate is 9% (or 0.09 as a decimal), and it is compounded quarterly, so n = 4. We need to calculate the amount after 4 years, so t = 4.
Using the formula, we can substitute the given values:
A = 5000(1 + 0.09/4)^(4*4)
Simplifying the equation:
A = 5000(1 + 0.0225)^(16)
A = 5000(1.0225)^(16)
Now, let's calculate it step by step:
A = 5000 * (1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225 * 1.0225)
A ≈ 5000 * 1.4318727
A ≈ $7,159.36
So, the amount after 4 years for Don Gecewicz's investment of $5000 at 9% interest compounded quarterly would be approximately $7,159.36.