You put $1,000 into your bank account with a 5% annual interest rate compounded quarterly. How much money will you have after three years?
To calculate the amount of money you will have after three years with a 5% annual interest rate compounded quarterly, you can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the future value or amount of money after the given time period
P is the principal amount (the initial deposit or investment) of $1,000
r is the annual interest rate in decimal form (5% is 0.05)
n is the number of times interest is compounded per year (quarterly means four times a year)
t is the number of years
Let's substitute the values into the formula:
A = 1000(1 + 0.05/4)^(4*3)
A = 1000(1 + 0.0125)^(12)
Next, we calculate the expression inside the parentheses first:
1 + 0.0125 = 1.0125
Now, we raise this value to the power of 12:
(1.0125)^12 ≈ 1.4025
Finally, multiply the result by the principal amount:
A = 1000 * 1.4025
A ≈ $1,402.50
After three years, you will have approximately $1,402.50 in your bank account.