Cogito
Consumer Math · Chapter 4 · Lesson 2
Loans and Amortisation
Where each payment actually goes.
12 problems · about 22 minutes · TEKS M.M.4.B
What this lesson teaches
The student analyses loan payments, separating interest from principal, and computes total cost.
- Each payment splits into interest for the month and principal.
- Early payments are mostly interest, because the balance is large.
- Total cost is payment times number of payments; a longer term costs more.
Warm Up
Straightforward practice. Get the method working first.
5 problems$10000 at 0.5% a month. Interest this month, in dollars?
Answer 50
Why $50.
Where does an extra payment go?
Answer Entirely to principal, cutting all future interest.
Why It reduces the balance directly.
APR 6%. Monthly rate in percent?
Answer 0.5
Why 6 ÷ 12.
$15000 at 0.5% a month. Interest in dollars?
Answer 75
Why 0.005 × 15000.
Payment $400, interest $100. Principal part in dollars?
Answer 300
Why 400 − 100.
Build It Up
The same ideas with more to keep track of.
3 problems$300 a month for 48 months. Total paid in dollars?
Answer 14400
Why 300 × 48.
Borrowed $12000, total paid $14400. Total interest in dollars?
Answer 2400
Why 14400 − 12000.
A longer term means a higher or lower total cost? 1 higher, 2 lower.
Answer 1
Why More months of interest.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each statement by where in a loan it applies.
Answer Early in the loan: Most of the payment is interest, The balance is near its largest · Late in the loan: Most of the payment is principal, The balance is nearly cleared
Why Interest is charged on the balance, which shrinks over time.
$500 a month for 36 months. Total paid in dollars?
Answer 18000
Why 500 × 36.
The Split: A $20000 balance at 0.5% a month. Interest this month, in dollars?
Answer 100 dollars
Why $100.
The Total: $400 a month for 60 months. Total paid, in dollars?
Answer 24000 dollars
Why $24000.