FM Annuities and Loan Amortization Flashcards

Under the sinking fund method of loan repayment, the borrower each period:

Answer: Pays interest only to the lender and deposits into a separate sinking fund

In the sinking fund method, the borrower pays interest on the full original loan to the lender and simultaneously accumulates principal in a separate fund.

If the sinking fund interest rate equals the loan interest rate, how do total periodic payments compare between the sinking fund and amortization methods?

Answer: Total periodic payments are identical under both methods

When both rates are equal, the total periodic payment (interest + sinking fund deposit) under the sinking fund method equals the level payment under amortization.

A $50,000 loan at 8% annual effective interest is amortized over 10 years with level annual payments. What is the interest component of the very first payment?

Answer: $4,000

Interest in the first period = outstanding balance × i = 50,000 × 0.08 = $4,000.

Using the retrospective method, the outstanding loan balance after k payments equals:

Answer: The original loan accumulated at rate i for k periods minus the accumulated value of k payments

Retrospective balance = L(1+i)^k - Payment × s(k,i), where s(k,i) is the accumulated value of payments made.

A $100,000 loan at 6% annual interest is amortized over 20 years with level annual payments. After 10 payments, approximately what percentage of the original balance remains outstanding?

Answer: 64%

Payment = 100,000/a(20,6%) ≈ $8,718; balance after 10 = 8,718 × a(10,6%) ≈ $64,162, which is about 64% of $100,000.

Which statement about the amortization method for a level-payment loan is CORRECT?

Answer: Early payments consist mostly of interest

In early periods the outstanding balance is large, so interest charges are high and only a small portion of the fixed payment reduces principal.

The principal repaid in the k-th payment of an amortizing loan (original loan L, n-period level payments, rate i) is given by:

Answer: (L / a(n,i)) × v^(n-k+1)

The k-th principal payment equals the level payment divided by the annuity factor times v^(n-k+1), i.e., (L/a(n,i)) × (1+i)^(-(n-k+1)).