Keep the rate basis explicit
All effective rates in this set compound annually unless the question explicitly names another basis. Dates are measured in years. The factors are fictional inputs. Identify the interval before selecting an answer.
Inspect the distractor assumption
Several incorrect choices are plausible if the end date is used as the interval length, a negative effective rate is treated as a negative factor, or an interpolation choice is presented as observed data. Explain which input changed rather than only recording the selected letter.
Try the questions
Da = 0.94 at year one and Db = 0.80 at year four. What is the annual effective implied forward for the interval?
- A.
17.5%
- B.
5.522715%
- C.
4.11408%
Answer and explanation
Answer: B
The interval lasts three years. Annualization uses power 1/3 on 0.94/0.80.
- A
This is total growth over three years, not its annual effective rate.
- B
Divide the factors, then take the cube root and subtract one.
- C
Using the four-year end date as the horizon ignores the one-year start.
A positive two-year factor equals 1.02. Which interpretation is consistent?
- A.
A positive payment has negative PV
- B.
The annual effective zero rate is negative
- C.
The factor must be deleted as impossible
Answer and explanation
Answer: B
The effective annual rate is 1.02^(−1/2)−1, below zero while the factor remains positive.
- A
Multiplying two positive numbers does not produce a negative present value.
- B
D above one corresponds to a negative effective accumulation rate.
- C
A factor above one is mathematically compatible with a negative rate.
Only one-year and two-year nodes are supplied. What is needed to price a payment at 1.5 years?
- A.
An explicitly supplied or modeled midpoint factor
- B.
The terminal coupon rate without a method
- C.
An assumption that all interpolation methods coincide
Answer and explanation
Answer: A
Specify the missing factor or a reproducible interpolation rule and retain its model status.
- A
The endpoints do not uniquely state the middle factor.
- B
A coupon label does not supply the missing zero factor.
- C
Different interpolation targets generally differ.