If Brad invests $2700 in an account paying 11% compounded quarterly. How much is in the account after 6 months?
2700*[1 + (0.11/4]^2 = $2850.54
Well, if Brad's money is being "compounded quarterly," I hope it's not growing any mushrooms in there! But let's get down to business, shall we?
To calculate the future value of the account after 6 months, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Future value
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case, Brad invested $2700 at an annual interest rate of 11%, compounded quarterly (4 times a year), and for 6 months (which is half a year). So let's do the math:
A = 2700(1 + 0.11/4)^(4 * 0.5)
A = 2700(1 + 0.0275)^(2)
A ≈ 2700 * 1.028071
A ≈ $2775.97
So, after 6 months of compounding interest like a champ, Brad will have approximately $2775.97 in his account. That's not clowning around!
To calculate the amount in the account after 6 months with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount in the account
P = initial principal (the amount initially invested)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years
In this case:
P = $2700
r = 11% or 0.11 (since the interest rate is given as a percentage)
n = 4 (since interest is compounded quarterly)
t = 6 months = 0.5 years
Plugging the values into the formula:
A = 2700(1 + 0.11/4)^(4*0.5)
A = 2700(1.0275)^2
A = 2700(1.05625625)
A ≈ $2854.88
Therefore, after 6 months, there would be approximately $2854.88 in the account.
To calculate the amount in Brad's account after 6 months with compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after time t
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the time in years
In this case, Brad invests $2700, the interest is compounded quarterly (n = 4), and the time is 6 months (0.5 years). The annual interest rate is 11%, which can be converted to a decimal by dividing by 100 (r = 0.11).
Using the formula, we can substitute the values:
A = 2700(1 + 0.11/4)^(4*0.5)
A = 2700(1 + 0.0275)^(2)
A = 2700(1.0275)^(2)
A = 2700 * 1.05500625
A ≈ $2,853.02
Therefore, after 6 months, there will be approximately $2,853.02 in Brad's account.