Perry's commission rate is 18%. He invests his commission from the sale of $8000 worth of merchandise at an interest rate of 11%, compounded quarterly. How much is Perry's investment worth after 6 months?
1520.29
To calculate Perry's investment worth after 6 months, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the total amount accumulated including interest
P = the principal amount (the initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the time the money is invested for (in years)
In this case, Perry's commission from the sale of $8000 worth of merchandise is the principal amount (P) and the interest rate (r) is 11% per year. The interest is compounded quarterly, so n = 4. The time invested (t) is 6 months, which is half a year.
First, let's convert the annual interest rate to decimal form:
r = 11% = 0.11
Next, let's calculate the total amount accumulated (A) after 6 months:
A = 8000 * (1 + 0.11/4)^(4 * 0.5)
A = 8000 * (1.0275)^2
A = 8000 * 1.05658125
A ≈ 8452.65
Therefore, Perry's investment is worth approximately $8452.65 after 6 months.