This document discusses different methods of calculating interest on loans and investments that are compounded over discrete time periods, such as weekly, monthly, or yearly. It provides formulas for calculating single payments, annual uniform payments, and uniform gradient payments. It also includes two examples, one calculating monthly loan payments over 36 months and the other calculating the value of a retirement account earning 8% annual interest over 35 years after initial contributions ended after 5 years.

1. Discrete Compounding and
payment
BY. YOSUF HASAN ALDRAZ

2. Contents
 Introduction
 Single payment
 Annual uniform payment
 Uniform Gradient payment
 Examples

3. Introduction
 Discrete compounding refers to the
method by which interest is calculated
and added to the principal at certain
set points in time ,For example,
interest may be compounded weekly,
monthly, or yearly .

4. Single payment
P = F(P/F, i%,
N)

5. Annual uniform payment
F = A(F/A, i%, N) A = F(A/F, i%, N)

6. Uniform Gradient payment
P = G (P/G, i%, N)
A = G (A/G, i%, N)

7. Example 1 :-
 You borrow $15,000 from your credit
union to purchase a used car. The
interest rate on your loan is 0.25% per
month∗ and you will make a total of 36
monthly payments. What is your
monthly payment?

8. solution

9. Example 2 :-
 When you take your first job, you decide
to start saving right away for your
retirement. You put $5,000 per year into
the company’s 401(k) plan, which
averages 8% interest per year. Five
years later, you move to another job and
start a new 401(k) plan. You never get
around to merging the funds in the two
plans. If the first plan continued to earn
interest at the rate of 8% per year for 35
years after you stopped making
contributions, how much is the account
worth?

10. solution

11. Thank you