1. Section 5.5
Situations where payment period and interest conversion period do not coincide are best handled from first principles rather than from developing formulas.
With an amortization schedule in which payments are made at a different frequency than interest is convertible, the following two-step procedure can be followed:
(1)
(2)
Find the rate of interest which is equivalent to the given rate of interest and convertible at the same frequency as payments are made.
Construct the amortization schedule with the rate of interest in step 1.
A similar approach can be used in the more complex situation where a sinking fund is involved with different frequencies for interest payments on the loan, sinking fund deposits, and interest conversion periods on the sinking fund.

2. A loan is being amortized with quarterly payments at annual effective rate of interest of 10%. If the amount of principal in the fifth payment is $1500, find the amount of principal in the 20th payment.
If X is the quarterly payment, then the entries in the column of the amortization table with principal repaid are
X(1/1.11/4)n , X(1/1.11/4)n–1 , X(1/1.11/4)n–2 , … ,
X(1/1.11/4)3 , X(1/1.11/4)2 , X(1/1.11/4) .
We have that X(1/1.11/4)n–4 = $ We want to find X(1/1.11/4)n–19 =
X(1/1.11/4)n–4 (1/1.11/4) 15 =
$1500(1.115/4) = $
Look at Example 5.9 on pages of the textbook.