FM Annuities and Loan Amortization Flashcards

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?

Answer: 4.2124

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

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

Answer: The beginning of each period

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

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

Answer: $12,000

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

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

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

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

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?

Answer: $2,590.09

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

In an amortization schedule for a fixed-payment loan, how does the principal component of each payment change over time?

Answer: Increases throughout the loan term

As the outstanding balance decreases, less interest is owed each period, so more of the fixed payment goes toward principal — the principal component increases.

Using the prospective method, the outstanding loan balance at any point in time equals:

Answer: The present value of all remaining future payments

The prospective method defines outstanding balance as the present value of all future scheduled payments discounted at the loan interest rate.