Applied Calculus in Finance Quiz

1. What is the growth rate of an investment A(t) = 2000e^(0.06t) (in dollars, t in years)?

a) 120e^(0.06t) dollars/year

b) 2000e^(0.06t) dollars/year

c) 0.06 dollars/year

d) 2000 dollars/year

2. For a cost function C(x) = 0.02x² + 4x + 500, what is the marginal cost at x = 50 units?

a) 6 dollars/unit

b) 8 dollars/unit

c) 4 dollars/unit

d) 10 dollars/unit

3. True or False: Marginal revenue is the derivative of the revenue function.

a) True

b) False

4. What is the marginal revenue for R(x) = 60x - 0.05x² at x = 300 units?

a) 30 dollars/unit

b) 45 dollars/unit

c) 60 dollars/unit

d) 15 dollars/unit

5. What is the present value of a $1000 cash flow in 5 years at a 3% discount rate?

a) 1000e^(-0.15) dollars

b) 1000e^(0.15) dollars

c) 1000 dollars

d) 1000e^(-0.03) dollars

6. In the Black-Scholes model, what does dC/dS represent for a call option?

a) Option price

b) Delta (sensitivity to stock price)

c) Time decay

d) Volatility

7. For a portfolio return R(w) = 0.07w + 0.02(1-w), what is dR/dw?

a) 0.05

b) 0.07

c) 0.02

d) 0.09

8. True or False: The present value of a continuous cash flow requires integration.

a) True

b) False

9. What is the rate of loan payoff for B(t) = 5000(1 - e^(-0.04t)) at t = 3 years?

a) 200e^(-0.12) dollars/year

b) 5000e^(-0.04) dollars/year

c) 200 dollars/year

d) 5000 dollars/year

10. For profit P(x) = -0.03x² + 15x - 800, where is the maximum profit?

a) x = 250 units

b) x = 500 units

c) x = 150 units

d) x = 800 units