FM FM Interest Rate Theory 2

Question 1

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

Accepted Answer

a_{n|i}

Answer

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:

Accepted Answer

(1 + i) × a_{n|}

Answer

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:

Accepted Answer

s_{n|} = ((1+i)^n − 1) / i

Answer

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:

Accepted Answer

1/i

Answer

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:

Accepted Answer

(ä_{n|} − n·v^n) / i

Answer

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

FM - Certifications in Financial Mathematics Practice Test