I'm having trouble trying to figure this problem out, I know the variables of the problem but I don't seem to get the right answer here is the formula that i'm using: A = P (1 + r/n)^n * t. Here is the problem:
If Joe deposits $12,000 into an account that yields 3% annual interest, how much will be in the account after 5 years if interest is compounded: quarterly.
I get around 13,000 but the answer is for 14,000, can anyone tell me what I'm doing wrong?
12000*(1+.03/4)20= about 14000
To solve this problem using the formula A = P(1 + r/n)^nt, you need to plug in the given values correctly.
Here's the step-by-step calculation:
1. Identify the values:
P = $12,000 (principal amount or initial deposit)
r = 3% (annual interest rate in decimal form, so r = 0.03)
n = 4 (number of times interest is compounded per year)
t = 5 (number of years)
2. Plug in the values into the formula:
A = 12000 * (1 + 0.03/4)^(4 * 5)
3. Simplify the calculation:
A = 12000 * (1 + 0.0075)^(20)
A = 12000 * (1.0075)^(20)
A ≈ 12000 * 1.159274259
A ≈ 13911.29 (rounded to two decimal places)
Therefore, the correct answer is approximately $13,911.29, not $14,000. Your calculated value of approximately $13,000 is incorrect.
It's possible that the answer provided to you is an approximation or was calculated differently. Keep in mind that small variations in compounded interest calculations can result in differences in the final amount over time.