FM FM Annuities and Loan Amortization

Question 1

What is the present value annuity factor a(5, 6%) for an ordinary annuity at an annual effective interest rate of 6% for 5 years?

Accepted Answer

4.2124

Answer

a(n,i) = (1 - v^n)/i = (1 - 1.06^-5)/0.06 = (1 - 0.74726)/0.06 = 4.2124.

Question 2

An annuity-due differs from an ordinary annuity (annuity-immediate) in that its payments occur at:

Accepted Answer

The beginning of each period

Answer

An annuity-due (denoted with a double-dot) makes payments at the start of each period, while an ordinary annuity pays at the end.

Question 3

A perpetuity-immediate pays $600 per year indefinitely. At an annual effective interest rate of 5%, what is the present value?

Accepted Answer

$12,000

Answer

The present value of a perpetuity-immediate is C/i = 600/0.05 = $12,000.

Question 4

Which formula correctly represents the accumulated value (future value) of an ordinary annuity of 1 per period for n periods at interest rate i?

Accepted Answer

s(n,i) = ((1+i)^n - 1) / i

Answer

The accumulation factor s(n,i) = ((1+i)^n - 1)/i represents the future value of an annuity-immediate paying 1 per period.

Question 5

A loan of $20,000 is repaid with equal annual payments over 10 years at an annual effective interest rate of 5%. What is the annual payment?

Accepted Answer

$2,590.09

Answer

Payment = L/a(10, 5%) = 20000/7.7217 = $2,590.09, where a(10, 5%) = (1 - 1.05^-10)/0.05.

FM - Certifications in Financial Mathematics Practice Test