The course Financial Math 1 includes 70 exercises that are performed individually or in small groups. Sample exercises are indicated here. In the course, you will learn how to solve problems like these—and many more! Note that some of the more challenging exercises address non-financial applications. These anticipate financial applications covered in Math 2 and Math 3. If these sample exercises are too easy, you may want to skip Math 1 and go straight to Math 2.

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Sample 2. Use your calculator to solve for x if

12 = 6^x

Sample 3. The present value of a $110 payment to be made one year from today is $100 with interest compounded quarterly.

a. What is the quarterly interest rate?
b. What would the equivalent continuous rate be?
c. What is the present value of the payment compounded continuously at that continuous rate?

Sample 4. Let f(x) = x³. Determine the equation for the tangent line at the point x = 0.

Sample 5. On May 14, 2002, we enter into a forward contract to deliver natural gas at the Permian Basin during the month of December 2002. We are to receive payment of $2.72 per million BTU on December 1.

a. What is the contract worth per million BTU on May 14?

b. On June 19, the forward price for December delivery of natural gas at the Permian Basin is $2.95. Assuming a continuously compounded (30/360) interest rate of 5%, what is the contract worth per million BTU today?

c. On December 1, 2002, the spot price of monthly Permian Basin natural gas is $3.05. How much is our contract now worth?

Sample 6.
a, Suppose today is April 23, 1999. The forward price for gold delivered in December is $290.70 per troy ounce. The spot price of gold is $283.30. What is the cost of carry for gold if there are 219 days until delivery (assume a 365 day year)?

b. On April 23, 1999, LIBOR was 5.10%. Comparing this to your cost of carry from (a), what conclusions might you draw?

Sample 7. A footpath intersects a narrow road at right angles. An observer stands on the path 100 feet from the road. A car drives down the road at a constant rate of 30 feet/second, passing the foot path. How fast is the distance between the observer and the car increasing when the car is 50 feet beyond the path? (Hint: Define your variables carefully. Represent rates with derivatives. Relate variables to one another using the Pythagorean Theorem. You will also need the chain rule.)

Sample 8. A portfolio has a duration of 5 years. If interest rates fall .05% (5 basis points), how much will the portfolio’s value change?

Sample 9. Find the following anti-derivative. Use the method of parts where appropriate. Check your answers by differentiating.