This document discusses amortization, which refers to the reduction of a debt over time through equal monthly payments of both principal and interest. It explains that as more principal is repaid each month, less interest is charged on the remaining balance. An amortization formula is provided to calculate monthly loan payments based on the principal, interest rate, and term of the loan. An example calculation is shown for a 30-year $225,000 mortgage loan at 3.25% interest.

1. Amortization
P R E S E N T E D B Y M R
S O O

2. Learning Intent
• To understand how monthly
payments for a loan is calculated,
considering bank interest rates and
time periods.

3. Curiosities

4. What is amortization
• Amortization refers to the reduction of a debt
over time by paying the same amount each
period, usually monthly. With amortization,
the payment amount consists of both
principal repayment and interest on the debt.
Principal is the loan balance that is still
outstanding.

5. How does it work?
• As more principal is repaid, less interest is
due on the principal balance. Over time,
the interest portion of each monthly
payment declines and the principal
repayment portion increases. Amortization
is most commonly encountered by the
general public when dealing with either
mortgage or car loans but (in accounting) it
can also refer to the periodic reduction in
value of any intangible asset over time.

17. Amortization Formula
• R =
𝑃𝑖
1−(1+𝑖)^−𝑛
• R = Repayments, Pi = Principal
• i =
𝑟 (𝑟𝑎𝑡𝑒)
𝑚 (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑡ℎ𝑒 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑖𝑠 𝑚𝑎𝑑𝑒 𝑖𝑛 𝑎 𝑦𝑒𝑎𝑟)
• n = m(Number of times the payment is made in a year) x t (number of years)

18. Amortization Example
• Find the monthly payment needed to amortize a loan of $225 000 at 3.25% for 30
years
R =
𝑃𝑖
1−(1+𝑖)^−𝑛 , R = Repayments, i =
0.0325
12
, n = 12x 30 = 360
R =
225000 𝑥
0.0325
12
1−(1+
0.0325
12
)^−360
=
609.375
1−0.37768979
= $979.0257
•

19. Let’s investigate a real-
life example!