Answer:
The compound interest on a sum of $12,000 at an 8% annual interest rate, compounded quarterly for 1 year, is approximately $989.19.
Explanation:
To calculate compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future amount (including principal and interest)
P = the principal amount (the initial sum of money) = $12,000
r = the annual interest rate (as a decimal) = 8% or 0.08
n = the number of times interest is compounded per year = 4 (quarterly)
t = the number of years = 1
Now, plug in the values and calculate:
A = 12000(1 + 0.08/4)^(4*1)
A = 12000(1 + 0.02)^4
A = 12000(1.02)^4
A ≈ 12000 * 1.082432
A ≈ 12,989.19
Now, calculate the compound interest by subtracting the principal amount from the future amount:
Compound Interest = A - P
Compound Interest = 12,989.19 - 12,000
Compound Interest ≈ $989.19
So, the compound interest on a sum of $12,000 at an 8% annual interest rate, compounded quarterly for 1 year, is approximately $989.19