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...
A(t)=P(1+ r/n)^nt
A(20) = 1000(1.013333)^80
= 1000 * 13.7795
= 1377.95
Don't know how you plugged in your numbers to get 1010.
Rats! I compounded 3x/year, not 4.
A(t)=P(1+ r/n)^nt
A(20) = 1000(1.01)^80
= 1000 * 2.21671
= 2216.71
An account with annual compound, apr of 2% and an initial deposit of 224, after 535 years
To find the correct answer, let's plug in the given values into the compound interest formula:
Principal amount, P = $1000
Annual interest rate, r = 4% or 0.04 (as a decimal)
Number of interest payments per year, n = 4 (quarterly)
Number of years, t = 20
So the formula becomes A(t) = P(1 + r/n)^(n*t).
Plugging in the values, we have:
A(20) = $1000(1 + 0.04/4)^(4*20)
= $1000(1 + 0.01)^(80)
= $1000(1.01)^80
Now, let's calculate the value using a calculator or spreadsheet:
A(20) ≈ $1000 * 1.8330408 ≈ $1833.04 (rounded to the nearest cent)
Therefore, the account balance after 20 years would be approximately $1833.04.