Carla invests $3,000, at 8% interest, compounded quarterly for 1 year. Manually calculate the compound interest for this investment.

3000(1+.08/4)^(4*1) - 3000 = 247.30

To manually calculate the compound interest for Carla's investment, we can use the formula:

A = P(1 + r/n)^(nt)

Where:
A is the total amount after interest.
P is the principal amount (initial investment).
r is the annual interest rate (as a decimal).
n is the number of times the interest is compounded per year.
t is the number of years.

In this case:
P = $3,000 (principal)
r = 8% = 0.08 (annual interest rate)
n = 4 (quarterly compounding)
t = 1 (1 year)

Let's substitute these values into the formula and calculate the compound interest step by step:

A = 3000(1 + 0.08/4)^(4*1)
= 3000(1 + 0.02)^4
= 3000(1.02)^4
= 3000(1.082432)
= $3,247.30

The compound interest for Carla's investment is $3,247.30 - $3,000 = $247.30.