FM Interest Rate Theory Flashcards

The present value of a level immediate annuity paying 1 per period for n periods at effective rate i is denoted:

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.

For a level annuity-due with n payments of 1 at effective rate i, the present value ä_{n|} equals:

Answer: (1 + i) × a_{n|}

An annuity-due has payments at the beginning of each period, so ä_{n|} = (1 + i) × a_{n|}.

The accumulated value at the end of n periods of a level immediate annuity of 1 per period is:

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.

A perpetuity-immediate paying 1 per year at effective annual rate i has a present value of:

Answer: 1/i

A perpetuity paying 1 per year forever at rate i has PV = 1/i, the sum of an infinite geometric series.

An increasing annuity (Ia)_{n|} at rate i pays 1, 2, 3, …, n at end of each period. Its present value equals:

Answer: (ä_{n|} − n·v^n) / i

(Ia)_{n|} = (ä_{n|} − n·v^n) / i, derived by summing the discounted increasing payments.

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%?

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%}.