Brianna invests $3,500, at 12% interest, compounded quarterly for 1 year. Manually calculate the compound interest for this investment.
3500((1+.12/4)^4 - 1) = 439.28
To manually calculate the compound interest for Brianna's investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
Let's plug the given values into the formula:
P = $3,500
r = 12% = 0.12 (converted to decimal)
n = 4 (quarters in a year)
t = 1 (year)
So the formula becomes:
A = 3500(1 + 0.12/4)^(4*1)
Now let's simplify and calculate the compound interest:
A = 3500(1 + 0.03)^4
A = 3500(1.03)^4
A = 3500(1.12550876)
A ≈ $3933.78
To find the compound interest, we subtract the initial investment from the future value:
Compound interest = A - P
Compound interest = $3933.78 - $3500
Compound interest ≈ $433.78
Therefore, the compound interest for Brianna's investment of $3,500 at a 12% interest rate, compounded quarterly for 1 year, is approximately $433.78.