Final answer:
To find the difference in interest earned at the end of the year, we can use the formula for compound interest. We will calculate the interest earned for each bank and then subtract the interest earned for Bank A from the interest earned for Bank B.
Step-by-step explanation:
In order to determine the difference in interest earned at the end of the year for $1000 invested in two different banks, we need to calculate the interest earned using the formula:
Interest = P(1 + r/n)^(nt) - P
Where:
- P is the principal amount (initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
For bank A with a 6% APR compounded semi-annually:
P = $1000, r = 0.06, n = 2, and t = 1
Interest = $1000(1 + 0.06/2)^(2 * 1) - $1000
Solving this equation gives us the interest earned for bank A.
For bank B with the same interest rate but compounded monthly:
P = $1000, r = 0.06, n = 12, and t = 1
Interest = $1000(1 + 0.06/12)^(12 * 1) - $1000
Solving this equation gives us the interest earned for bank B.
Finally, subtract the interest earned for bank A from the interest earned for bank B to find the difference.