Jim opens a savings account with a deposit of $10,000. If the account has an annual interest rate of 6%, compounded quarterly, how much is in the account after one year? (Assume that he does not make any withdrawals. Round only your final answer to the nearest cent.)
what is 10000(1.015)^4 ??
To calculate the amount in the account after one year with compound interest, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, we have:
P = $10,000
r = 6% = 0.06 (converted to a decimal)
n = 4 (compounded quarterly)
t = 1 year
Substituting these values into the formula, we get:
A = $10,000(1 + 0.06/4)^(4*1)
Now, let's simplify the equation and calculate the future value:
A = $10,000(1 + 0.015)^4
A = $10,000(1.015)^4
A = $10,000(1.061676)
A ≈ $10,616.76
Therefore, the amount in the account after one year, rounded to the nearest cent, is approximately $10,616.76.