interest 7%; investment $2000, compounded monthly - how much after 10 years. I am very close on this one but must be missing an important step:
A(t) = 2,000(1 + .07/12)^(10)(12)
A(10) = 2,000(1.0058)^120
A(10) = 2,000(2.0017 = 4003.4
However the answer is actual $4220.29
What have I done wrong??
you should have not rounded the 7/12.
Put this into the google search window:
2,000(1 + .07/12)^(120)
In your calculation, you made a mistake when calculating the monthly interest rate and the number of compounding periods. Let me explain the correct steps to calculate the final amount after 10 years using compound interest.
To calculate compound interest, you need to use the following formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount after time t
P is the principal amount (initial investment)
r is the interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In your case, the principal amount is $2000, the interest rate is 7% (or 0.07 as a decimal), and the interest is compounded monthly, so n = 12.
Remember to also adjust the interest rate to reflect the monthly compounding. So, the correct monthly interest rate would be 0.07/12.
Now, let's calculate:
A = 2000(1 + 0.07/12)^(10*12)
A = 2000(1.00583)^120
Calculating this correctly yields:
A ≈ $4,220.29
So, the correct answer for the final amount after 10 years, compounded monthly with an interest rate of 7%, for an initial investment of $2000, is approximately $4,220.29.
Therefore, you made a mistake in your calculation of the monthly interest rate and the exponent. Correcting those errors will give you the correct answer.