Hong has 4000 to invest. she invests 2000 at a rate of 2.5% per year simple interest. she also invests 2000 at a rate of 2% per year compound interest. find the value of each investement at the end of 8 years.

First, let's calculate the value of the simple interest investment.

Simple interest is calculated using the formula: I = PRT, where I is the interest, P is the principal amount (initial investment), R is the annual interest rate (in decimal form), and T is the time the money is invested for in years.

In this case, P = $2000, R = 2.5/100 = 0.025 (to convert the percentage into a decimal), and T = 8 years.

So, I = 2000 * 0.025 * 8 = $400.

The value of the investment at the end of 8 years is the initial principal plus the interest, so $2000 +$400 = $2400.

Next, let's calculate the value of the compound interest investment.

Compound interest is calculated using the formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

In this case, P = $2000, r = 2/100 = 0.02, n = 1 (since it doesn't specify otherwise, we'll assume that interest is compounded once per year), and t = 8 years.

So, A = 2000 * (1 + 0.02/1)^(1*8) = $2000 * (1.02)^8 =$2371.86.

So, the value of the first investment after 8 years is $2400, and the value of the second investment after 8 years is approximately$2371.86.