FM FM Annuities and Loan Amortization 1 — Questions and Answers
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?
- 4.2124 (Correct answer)
- 4.4651
- 3.9927
- 5.6371
Correct answer: 4.2124
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:
- The end of each period
- The beginning of each period (Correct answer)
- Random intervals within each period
- Annual intervals only, regardless of compounding frequency
Correct 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.
Question 3: A perpetuity-immediate pays $600 per year indefinitely. At an annual effective interest rate of 5%, what is the present value?
- $10,200
- $12,000 (Correct answer)
- $11,429
- $9,800
Correct answer: $12,000
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?
- s(n,i) = ((1+i)^n - 1) / i (Correct answer)
- a(n,i) = (1 - (1+i)^-n) / i
- s(n,i) = ((1+i)^n - 1) / d
- ä(n,i) = (1 - (1+i)^-n) / d
Correct 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.
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?
- $2,312.20
- $2,590.09 (Correct answer)
- $2,800.00
- $2,443.67
Correct 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.
Question 6: In an amortization schedule for a fixed-payment loan, how does the principal component of each payment change over time?
- Decreases throughout the loan term
- Remains constant each period
- Increases throughout the loan term (Correct answer)
- Fluctuates based on remaining interest accrued
Correct 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.
Question 7: Using the prospective method, the outstanding loan balance at any point in time equals:
- The original loan amount minus cumulative principal paid
- The present value of all remaining future payments (Correct answer)
- The future value of all payments already made
- The original loan amount plus total accrued interest
Correct 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.
FM FM Annuities and Loan Amortization 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?