FM FM Annuities and Loan Amortization 2

Question 1

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

Accepted Answer

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

Answer

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.

Question 2

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

Accepted Answer

Total periodic payments are identical under both methods

Answer

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

Question 3

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?

Accepted Answer

$4,000

Answer

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

Question 4

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

Accepted Answer

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

Answer

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

Question 5

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?

Accepted Answer

64%

Answer

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.

FM - Certifications in Financial Mathematics Practice Test

FM - Certifications in Financial Mathematics Practice Test

FM FM Annuities and Loan Amortization 2