use the compound interest formula

A=P(1+r/n)^nt and A=Pe^rt to solve

1-Find the accumulated value of an investment of $5000 at 9% compounded continuously for 6 years.

2-Find for an investment of $700 at 16% compounded quarterly for 2 years.

To solve these problems using the compound interest formulas, we need to plug in the given values into the formulas and compute the final accumulated value.

Let's start with the first problem:
1. Find the accumulated value of an investment of $5000 at 9% compounded continuously for 6 years.

Using the formula A = Pe^(rt), we can apply it to this problem as follows:
A = 5000e^(0.09*6) (where A is the final accumulated value, P is the initial principal, r is the interest rate per year, and t is the number of years)

Now, we can calculate the accumulated value:
A = 5000 * e^(0.54)
A ≈ 5000 * 1.7183
A ≈ $8,591.50

Therefore, the accumulated value of the investment after 6 years will be approximately $8,591.50.

Now let's move on to the second problem:
2. Find the accumulated value for an investment of $700 at 16% compounded quarterly for 2 years.

Using the formula A = P(1 + r/n)^(nt), we can apply it to this problem:
A = 700 * (1 + (0.16/4))^(4*2) (where A is the final accumulated value, P is the initial principal, r is the interest rate per year, n is the number of compounding periods per year, and t is the number of years)

Now we can calculate the accumulated value:
A = 700 * (1.04)^(8)
A ≈ 700 * 1.3605
A ≈ $952.35

Therefore, the accumulated value of the investment after 2 years will be approximately $952.35.

By using the compound interest formulas and plugging in the appropriate values, we were able to calculate the accumulated values for these investments.