The one-year forward rates, deferred t years, are estimated to be:

Calculate the spot rate for a zero-coupon bond maturing three years from now.

• 4%
• 5%
• 6%
• 7%
• 8%

Annuity A pays 1 at the beginning of each year for three years. Annuity B pays 1 at the beginning of each year for four years. The Macaulay duration of Annuity A at the time of purchase is 0.93. Both annuities offer the same yield rate.

Calculate the Macaulay duration of Annuity B at the time of purchase.

• 1.240
• 1.369
• 1.500
• 1.930
• 1.965

Cash flows are 40,000 at time 2 (in years), 25,000 at time 3, and 100,000 at time 4. The annual effective yield rate is 7.0%.

Calculate the Macaulay duration.

• 2.2
• 2.3
• 3.1
• 3.3
• 3.4

Rhonda purchases a perpetuity providing a payment of 1 at the beginning of each year. The perpetuity’s Macaulay duration is 30 years.

Calculate the modified duration of this perpetuity

• 28.97
• 29.00
• 29.03
• 29.07
• 29.10

A bank accepts a 20,000 deposit from a customer on which it guarantees to pay an annual effective interest rate of 10% for two years. The customer needs to withdraw half of the accumulated value at the end of the first year. The customer will withdraw the remaining value at the end of the second year. The bank has the following investment options available, which may be purchased in any quantity:

Bond H: A one-year zero-coupon bond yielding 10% annually

Bond I: A two-year zero-coupon bond yielding 11% annually

Bond J: A two-year bond that sells at par with 12% annual coupons

Any portion of the 20,000 deposit that is not needed to be invested in bonds is retained by the bank as profit. Determine which of the following investment strategies produces the highest profit for the bank and is guaranteed to meet the customer’s withdrawal needs.

• 9,091 in Bond H, 8,264 in Bond I, 2,145 in Bond J
• 10,000 in Bond H, 10,000 in Bond I
• 10,000 in Bond H, 9,821 in Bond I
• 8,910 in Bond H, 731 in Bond I, 10,000 in Bond J
• 8,821 in Bond H, 10,804 in Bond J

A company is considering investing in a particular project. The project requires an investment of X today. Additional investments are required at the beginning of each of the next five years, with each year’s investment 5% greater than the previous year’s investment. The investment is expected to produce an income of 100 per year at the end of each year forever, with the first payment expected at the end of the first year. At an annual effective interest rate of 10.25%, the project has a net present value of zero.

Calculate X.

• 183
• 192
• 205
• 215
• 225

An insurer enters into a four-year contract today. The contract requires the insured to deposit 500 into a fund that earns an annual effective rate of 5.0%, and from which all claims will be paid. The insurer expects that 100 in claims will be paid at the end of each year, for the next four years. At the end of the fourth year, after all claims are paid, the insurer is required to return 75% of the remaining fund balance to the insured. To issue this policy, the insurer incurs 100 in expenses today. It also collects a fee of 125 at the end of two years.

Calculate the insurer’s yield rate.

• 9%
• 24%
• 39%
• 54%
• 69%

An investor buys a perpetuity-immediate providing annual payments of 1, with an annual effective interest rate of i and Macaulay duration of 17.6 years.

Calculate the Macaulay duration in years using an annual effective interest rate of 2i instead of i.

• 8.8
• 9.3
• 9.8
• 34.2
• 35.2

An investor purchases two bonds. The bonds have the same annual effective yield rate i, with i > 0. With respect to the annual effective yield rate, their modified durations are a years and b years, with 0 < a < b. One of these two bonds has a Macaulay duration of c years, with a < c < b.

Determine which of the following is an expression, in years, for the Macaulay duration of the other bond.

• bc/a
• ac/b
• ab/c
• b + c – a
• a + c – b

Company X received the approval to start no more than two projects in the current calendar year. Three different projects were recommended, each of which requires an investment of 800 to be made at the beginning of the year.

The cash flows for each of the three projects are as follows

The company uses an annual effective interest rate of 10% to discount its cash flows. Determine which combination of projects the company should select.

• Projects A and B
• Projects B and C
• Projects A and C
• Project A only
• Project B only