A man invests $10, 000 in an account that pays 8.5% interest per year, compounded quarterly.
What is the amount of money that he will have after 3 years
a = 10000 [1 + (.085 / 4)]^(3 * 4)
To find the amount of money that the man will have after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
P = the principal amount (initial investment)
r = annual interest rate (written as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $10,000
r = 8.5% = 0.085 (converted into a decimal)
n = 4 (compounded quarterly)
t = 3 years
Now we can substitute these values into the formula and solve for A:
A = $10,000(1 + 0.085/4)^(4*3)
Using a calculator or a spreadsheet, we can evaluate the expression inside the parentheses first, then raise it to the power of 12 (4 * 3):
A = $10,000(1 + 0.02125)^(12)
A = $10,000(1.02125)^(12)
Next, we raise 1.02125 to the power of 12:
A ≈ $10,000(1.3458825)
Finally, we multiply $10,000 by 1.3458825:
A ≈ $13,458.825
Therefore, the man will have approximately $13,458.825 after 3 years.