Use the compound interest formula to compute the total amount accumulated and the interest earned.
$3000 for 3 years at 4.0% compounded
annually.
The compound interest formula is:
A = P(1 + r/n)^(nt)
Where:
A = total amount accumulated
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
In this case, we have:
P = $3000
r = 0.04 (4.0% expressed as a decimal)
n = 1 (compounded annually)
t = 3 years
So we can plug these values into the formula:
A = 3000(1 + 0.04/1)^(1*3)
A = 3000(1.04)^3
A = 3000(1.124864)
A = $3,374.59
The total amount accumulated after 3 years is $3,374.59.
To calculate the interest earned, we just subtract the initial investment from the total amount accumulated:
I = A - P
I = $3,374.59 - $3000
I = $374.59
So the interest earned is $374.59.
To compute the total amount accumulated and the interest earned, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = total amount accumulated
P = principal amount (initial amount) = $3000
r = annual interest rate (as a decimal) = 4.0% = 0.04
n = number of times interest is compounded per year (assuming annually, n = 1)
t = number of years = 3
Substituting the values into the formula:
A = 3000(1 + 0.04/1)^(1*3)
Calculating the values within parentheses first:
A = 3000(1 + 0.04)^(3)
Adding 1 to 0.04:
A = 3000(1.04)^(3)
Calculating the exponent:
A = 3000(1.124864)
Multiplying:
A ≈ 3374.59
Therefore, the total amount accumulated is approximately $3374.59.
To find the interest earned, we can subtract the principal amount from the total amount accumulated:
Interest Earned = Total Amount Accumulated - Principal Amount
Interest Earned = 3374.59 - 3000
Interest Earned ≈ $374.59
Therefore, the interest earned is approximately $374.59.