At the beginning of each year, Joe invests $10,000 in his retirement fund. The fund gives 10% interestm compouned annually. At the end of the third year, how much money will be in Joe's fund?
THIS IS AN AOPS PROBLEM YOU CHEATER!!!
To calculate the amount of money in Joe's retirement fund at the end of the third year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial amount)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case, Joe invests $10,000 at an interest rate of 10% (0.10) compounded annually for 3 years.
Plugging the values into the formula:
A = 10,000(1 + 0.10/1)^(1*3)
Simplifying the equation:
A = 10,000(1 + 0.10)^3
Now we can calculate the value:
A = 10,000(1.10)^3
Calculating the exponent:
A = 10,000(1.331)
Finally, we multiply:
A ≈ $13,310.00
Therefore, at the end of the third year, there will be approximately $13,310.00 in Joe's retirement fund.
first 10,000 for 3 years
10,000 (1.10)^3
then second year deposit
10,000 (1.10)^2
then
10,000 (1.10)
or
10,000 (1.1^3 + 1.1^2 + 1.1)