Help....Help...
Suppose you deposit a principal amount of p dollars in a bank account that pays compound interest. If the annual interest rate r (expressed as a decimal) and the bank makes interest payments n times every year, the amount of money A you would have after t years is given by
Find the account balance after 20 years if you started with a deposit of $1000, and the bank was paying 4% interest compounded quarterly (4 times a year). Round your answer to the nearest cent.
I used the formula A(t)=P(1+ r/n)nt
and got 1010 and this is not the correct answer...
To find the correct account balance, we need to apply the correct values to the formula.
In this case, the principal amount (P) is $1000, the annual interest rate (r) is 4% (or 0.04 in decimal form), the number of interest payments per year (n) is 4 (quarterly payments), and the number of years (t) is 20.
Now, let's substitute these values into the formula:
A(t) = P(1 + r/n)^(n*t)
A(20) = $1000(1 + 0.04/4)^(4*20)
A(20) = $1000(1 + 0.01)^(80)
A(20) = $1000(1.01)^80
Now, we can use a calculator to evaluate this expression:
A(20) ≈ $1000 * 2.2080403
Rounding the answer to the nearest cent, the account balance after 20 years would be approximately $2,208.04.
Therefore, the correct answer is $2,208.04, not $1,010 as you calculated incorrectly.
Let me know if you need help with anything else!