Question

If 28500 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. (a) Annual: Your answer is (b) Semiannual: Your answer is (c) Monthly: Your answer is (d) Daily: Your answer is (e) Continuously: Your answer is Note: You can earn partial credit on this problem.

Answer 1

Your question isn't very clear so I put it in the description.

Explanation:

The value of an investment at the end of a period can be calculated using the formula A = P(1 + r/n)^(nt), where A is the future value, P is the initial principal balance, r is the interest rate, n is the number of times the interest is compounded per unit time and t is the time in years.

For an initial investment of $28,500 at an interest rate of 7% per year for 5 years:

a. Annual compounding: n = 1, so A = 28500(1 + 0.07/1)^(1*5) = $39,873.43.

b. Semiannual compounding: n = 2, so A = 28500(1 + 0.07/2)^(2*5) = $40,136.24.

c. Monthly compounding: n = 12, so A = 28500(1 + 0.07/12)^(12*5) = $40,386.75.

d. Daily compounding: n = 365, so A = 28500(1 + 0.07/365)^(365*5) = $40,440.95.

e. Continuous compounding: The formula for continuous compounding is A = Pe^(rt), where e is Euler’s number (approximately 2.718). So A = 28500 * e^(0.07*5) = $40,455.64.