Calculate the interest earned when $40 000 is invested for 6 years at 9% pa compounded each 6 months

Sure, here's how you can calculate the interest earned:

Step 1: Understand the terms

• Principal amount (P) = $40,000
• Time period (t) = 6 years
• Annual interest rate (r) = 9% or 0.09
• Number of times interest is compounded per year (n) = 2 (since it's compounded every 6 months)

Step 2: Convert the annual interest rate to the rate per period The rate per period (r/n) = 0.09/2 = 0.045

Step 3: Convert the time period to the number of total periods The total number of periods (nt) = 6*2 = 12

Step 4: Use the formula for compound interest to calculate the total amount (A) after 6 years A = P(1 + r/n)^(nt) A = $40,000(1 + 0.045)^12

Step 5: Calculate the total amount A = $40,000 * (1.045)^12 A =$40,000 * 1.707364 A = $68,294.56

Step 6: Subtract the initial principal from the total amount to find the interest earned Interest = A - P Interest = $68,294.56 -$40,000 Interest = $28,294.56

So, the interest earned when $40,000 is invested for 6 years at 9$28,294.56.