Final answer:
The difference in the value after 10 years of an initial investment of $2,000 at 5% annual interest compounded quarterly instead of annually is $45.45.
Step-by-step explanation:
The difference in the value after 10 years of an initial investment of $2,000 at 5% annual interest when the interest is compounded quarterly rather than annually can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal amount is $2,000, the annual interest rate is 5%, and the interest is compounded quarterly, which means n = 4.
When the interest is compounded annually, n = 1 and the formula becomes A = 2000(1 + 0.05/1)^(1*10) = $3,256.25.
When the interest is compounded quarterly, n = 4 and the formula becomes A = 2000(1 + 0.05/4)^(4*10) = $3,301.70.
Therefore, the difference in the value after 10 years is $3,301.70 - $3,256.25 = $45.45.