Problem 1:You invest $4,000 at an annual interest rate of 5% compounded continuously. How much will you have after 2 years?*4 points$4420.68$4320.68$4220.68$4120.68Problem 2:You borrow $6,500 at an annual interest rate of 8% compounded continuously. What will be the total amount owed after 3 years?*4 points$8261.12$8262.12$8263.12$8264.12Problem 3:If you deposit $10,000 in a savings account that earns 3.5% interest annually, compounded continuously, how much will you have after 4 years?*4 points$11501.74$11502.74$11503.74$11504.74Problem 4:You take out a loan of $8,000 with an annual interest rate of 6% compounded continuously. How much will you owe after 2.5 years?*4 points$9291.67$9292.67$9293.67$9294.67Problem 5:An investment of $7,500 is made at an annual interest rate of 4%, compounded continuously. Calculate the value of the investment after 5 years.*4 points$9160.52$9260.52$9360.52$9460.52

Problem 1: To calculate the amount you will have after 2 years, we can use the formula for continuous compound interest: A = P * e^(rt), where A is the final amount, P is the principal amount, e is the base of the natural logarithm, r is the interest rate, and t is the time in years.

In this case, the principal amount is $4,000, the interest rate is 5% (or 0.05 as a decimal), and the time is 2 years. Plugging these values into the formula, we get:

A = 4000 * e^(0.05 * 2)

Using a calculator, we find that e^(0.05 * 2) is approximately 1.1025. Multiplying this by $4,000, we get:

A = 4000 * 1.1025 = $4405

Therefore, you will have approximately $4405 after 2 years.

Problem 2: To calculate the total amount owed after 3 years, we can again use the formula for continuous compound interest: A = P * e^(rt).

In this case, the principal amount is $6,500, the interest rate is 8% (or 0.08 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:

A = 6500 * e^(0.08 * 3)

Using a calculator, we find that e^(0.08 * 3) is approximately 1.2597. Multiplying this by $6,500, we get:

A = 6500 * 1.2597 = $8198.05

Therefore, the total amount owed after 3 years will be approximately $8198.05.

Problem 3: To calculate the amount you will have after 4 years, we can once again use the formula for continuous compound interest: A = P * e^(rt).

In this case, the principal amount is $10,000, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 4 years. Plugging these values into the formula, we get:

A = 10000 * e^(0.035 * 4)

Using a calculator, we find that e^(0.035 * 4) is approximately 1.1507. Multiplying this by $10,000, we get:

A = 10000 * 1.1507 = $11507

Therefore, you will have approximately $11507 after 4 years.

Problem 4: To calculate the amount you will owe after 2.5 years, we can use the formula for continuous compound interest: A = P * e^(rt).

In this case, the principal amount is $8,000, the interest rate is 6% (or 0.06 as a decimal), and the time is 2.5 years. Plugging these values into the formula, we get:

A = 8000 * e^(0.06 * 2.5)

Using a calculator, we find that e^(0.06 * 2.5) is approximately 1.1642. Multiplying this by $8,000, we get:

A = 8000 * 1.1642 = $9313.60

Therefore, you will owe approximately $9313.60 after 2.5 years.

Problem 5: To calculate the value of the investment after 5 years, we can use the formula for continuous compound interest: A = P * e^(rt).

In this case, the principal amount is $7,500, the interest rate is 4% (or 0.04 as a decimal), and the time is 5 years. Plugging these values into the formula, we get:

A = 7500 * e^(0.04 * 5)

Using a calculator, we find that e^(0.04 * 5) is approximately 1.2214. Multiplying this by $7,500, we get:

A = 7500 * 1.2214 = $9160.50

Therefore, the value of the investment after 5 years will be approximately $9160.50.