math

A. The accumulated value of the investment when compounded semiannually for 4 years at 5% interest is $28,657.50. This can be calculated using the formula A = P(1 + r/n)^(nt) where P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the length of the investment. B. The accumulated value of the investment when compounded quarterly for 4 years at 5% interest is $28,789.36. This is calculated using the same formula as above, but changing the number of compounding periods per year from semiannual to quarterly. C. The accumulated value of the investment when compounded monthly for 4 years at 5% interest is $28,888.54. Again, this is calculated using the same formula as above, but changing the number of compounding periods per year from quarterly to monthly. D. The accumulated value of the investment when compounded continuously for 4 years at 5% interest is $29,069.01. This is calculated using the formula A = Pe^(rt) where P is the principal, r is the interest rate, and t is the length of the investment. Continuous compounding is different than other forms of compounding because the compounding occurs continuously rather than at periodic intervals. This means that the return on the investment capital accumulates faster than if it were compounded at regular intervals