FM FM Interest Rate Theory 2 — Questions and Answers
Question 1: The present value of a level immediate annuity paying 1 per period for n periods at effective rate i is denoted:
- a_{n|i} (Correct answer)
- ä_{n|i}
- s_{n|i}
- s̈_{n|i}
Correct answer: a_{n|i}
a_{n|i} denotes the present value of a level ordinary annuity (payments at end of period) of 1 per period for n periods.
Question 2: For a level annuity-due with n payments of 1 at effective rate i, the present value ä_{n|} equals:
- (1 + i) × a_{n|} (Correct answer)
- a_{n|} / (1 + i)
- a_{n|} − 1
- a_{n|} × d
Correct answer: (1 + i) × a_{n|}
An annuity-due has payments at the beginning of each period, so ä_{n|} = (1 + i) × a_{n|}.
Question 3: The accumulated value at the end of n periods of a level immediate annuity of 1 per period is:
- s_{n|} = ((1+i)^n − 1) / i (Correct answer)
- s_{n|} = (1 − v^n) / i
- s_{n|} = a_{n|} × (1+i)^n × i
- s_{n|} = n / (1+i)
Correct answer: s_{n|} = ((1+i)^n − 1) / i
The future value (accumulated value) of an ordinary annuity is s_{n|} = ((1+i)^n − 1) / i.
Question 4: A perpetuity-immediate paying 1 per year at effective annual rate i has a present value of:
- 1/i (Correct answer)
- 1/d
- i
- d/i
Correct answer: 1/i
A perpetuity paying 1 per year forever at rate i has PV = 1/i, the sum of an infinite geometric series.
Question 5: An increasing annuity (Ia)_{n|} at rate i pays 1, 2, 3, …, n at end of each period. Its present value equals:
- (ä_{n|} − n·v^n) / i (Correct answer)
- (a_{n|} + n·v^n) / i
- n·a_{n|} / i
- a_{n|} × n
Correct answer: (ä_{n|} − n·v^n) / i
(Ia)_{n|} = (ä_{n|} − n·v^n) / i, derived by summing the discounted increasing payments.
Question 6: Under the FM exam, what is the present value of a deferred annuity that pays 1 per year for 10 years, with the first payment at the end of year 6, at i = 5%?
- v^5 × a_{10|5%} (Correct answer)
- v^6 × a_{10|5%}
- a_{15|5%} − a_{5|5%}
- a_{10|5%} − a_{5|5%}
Correct answer: v^5 × a_{10|5%}
A deferred annuity with first payment at end of year 6 is discounted 5 years: PV = v^5 × a_{10|5%}.
FM FM Interest Rate Theory 2
The present value of a level immediate annuity paying 1 per period for n periods at effective rate i is denoted: