This document provides an overview of interest calculations and inventory models. It begins by defining simple and compound interest, and provides formulas for calculating interest in both cases. It then discusses inventory order quantity models, including economic order quantity (EOQ) and economic batch quantity (EBQ) models. The EOQ model aims to determine the optimal order quantity to minimize total inventory costs, including ordering and holding costs. The EBQ model determines optimal batch size when production is done in batches. Several examples of problems are provided for both models with and without shortages.

1. UNIT 5
Interest Calculations &
Inventory Models
Mr.T.SOMASUNDARAM
ASSISTANT PROFESSOR
DEPARTMENT OF MANAGEMENT
KRISTU JAYANTI COLLEGE,
BANGALORE

2. UNIT 5
Interest Calculations & Inventory
Models
Simple Interest, Compound Interest
including half yearly and quarterly
calculations, Inventory Models – EOQ
and EBQ Models (with and without
shortage)

3. INTEREST
Definition:
“Interest is the compensation received by the lender
of money from the borrower, calculated at a specific rate
percent and for a specified time, on the sum of money lent
by the lender to the borrower.”
Simple Interest:
“A Simple interest approach considers that the
interest earned is a linear functions of time, with the
original sum lent (i.e.) principal and the rate of interest
remaining constant. Simple interest earned directly varies
with the time.”
Total Interest = Future Value – Present Value

4. Formula - Simple Interest (S.I.):
I = F – P
Thus, F = P [1+ r n]
where P is the principal ( or present value of money
lent).
n – Number of periods of which the money is lent.
r – rate of interest percent per annum, expressed as a
decimal.
I – rupees of interest earned for the interest period.
F – Amount to be received (Future value) at the end of
‘n’ periods.

5. Exact and Ordinary Simple Interest:
Exact Simple Interest – it is calculated on the basis of
a 365 day in a year (366 days in case of leap year).
Ordinary Simple Interest – it is calculated on the basis
of a 360 day in a year.
Exact and Approximate Time:
Exact time – it is the actual number of days as found
from a calendar.
Approximate time – it is found by assuming each
month to have only 30 days.
Important terms in S.I.

6. Important terms in S.I.

7. Exercise Problems:
1. Find the simple interest for the amount of Rs.1000
a) At 4.5% per annum for 1 year.
b) At 5% per annum for 10 months.
2. At what rate of simple interest will Rs.4000 amount
to Rs.4220 in one year?
3. In what time will Rs.6000 amount to Rs.6375 at 5%
simple interest?
4. What amount is required to repay a loan of Rs.300
for 7 months at 12.5% per annum?
Problems on Simple Interest (S.I.)

8. Classwork Problems:
1. Find the simple interest for the amount of Rs.1000
a) At 3.5% per annum for 6 months.
b) At 6% per annum for 8 months.
2. At what rate of simple interest will Rs.1440 amount
to Rs.1488 in 10 months?
3. In what time will Rs.90 amount to Rs.105.75 at 5%
simple interest?
4. Determine the principal which will amount to
Rs.13000 in 6 years at 5% per annum.
Problems on Simple Interest (S.I.)

9. Homework Problems:
1. Calculate the simple interest on Rs.500 for 5 years
at 6% per annum.
2. Find the amount of Rs.3000 at 5 ½ % per annum in
4 ½ years.
3. Find the period in which Rs.5500 will amount to
Rs.6050 at 4% per annum.
4. Calculate the rate of interest at which Rs.750 will
amount to Rs.825 in 5 years.
Problems on Simple Interest (S.I.)

10. Exercise Problems:
1. Using Banker’s Rule, find the simple interest on
Rs.4000 at 6% from March 21, 2004 to July 24, 2004.
2. How much will a banker charge as interest on
Rs.5000 at 6% p.a. from 20th April 2004 to 1st July
2004.
3. Using Banker’s rule, find the simple interest on
Rs.5000 at 4.75% for 80 days.
Problems on Banker’s Rule

11. Compound Interest
Definition:
“It is the approach assumes that the interest earned
is not withdrawn at the end of the interest period
but is added, automatically, to the original sum lent
to constitute the principal for the second interest
period. This process is repeated for the entire time
period ‘n’ and the total interest thus accumulated is
called the “compound interest”.
Formula:
i) To find amount due after ‘n’ years, F = P (1 + r)n

13. Nominal and Effective Rate of Interest:
“Nominal rate of interest is the rate of interest
received when the conversion period is one year.”
Formula:
where R is rate of interest.
r is effective rate of interest.
q is no. of times interest is computed in a year.

14. Exercise Problems:
1. Find the amount of Rs.5500 in 8 years at 12% per
annum interest compounded.
2. Calculate the compound interest on Rs.7500 at 14%
for 4 years.
3. Find the compound interest on Rs.4000 for 1.5
years at 10% per annum payable half – yearly.
4. Find the C.I. on Rs.26736 for ¾ years at 16% per
annum payable every 3 months.
5. Find the C.I. on Rs.36000 for 2 years at 24% per
annum payable every month.
Problems on Compound Interest
(C.I.)

15. Classwork Problems:
1. Calculate amount & interest on Rs.1000 for 20
years at 5% compound interest.
2. Find the interest on Rs.1000 at 4% per annum
compounded annually for 5 ½ years.
3. What is the present value of Rs.1000 due after 1
year if the compound interest is reckoned at 12%?
What will be the present value if simple interest is
allowed instead of compound interest? Do you find
any difference? What are the reasons?
Problems on Compound Interest
(C.I.)

16. Homework Problems:
1. Calculate the amount and compound interest on
Rs.100 for 15 years, allowing compound interest at the
rate of 12% per annum.
2. What principal invested today will amount to
Rs.1630.80 in 4 years at 13% per annum compound
interest.
3. Find in how many years Rs.300 will become
Rs.3000 at 9% per annum compound interest?
Problems on Compound Interest
(C.I.)

17. Homework Problems:
4. Find the C.I. on Rs.8000 for 3 years at 5% per
annum payable half – yearly.
5. Find the C.I. on Rs.5000 for 3 years at 5% per
annum payable every 3 months.
6. Find the C.I. on Rs.65000 for 3 years at 6% per
annum payable every month.
Problems on Compound Interest
(C.I.)

18. Inventory Models - EOQ
Economic Order Quantity (EOQ):
Economic order quantity (EOQ) is the order size
that minimizes the sum of ordering and holding costs
related to raw materials or merchandise inventories. In
other words, it is the optimal inventory size that should be
ordered with the supplier to minimize the total annual
inventory cost of the business. Other names used for
economic order quantity are optimal order size and
optimal order quantity.
EOQ means the quantity produced or procured
during one production cycle. It is the size of order which
minimizes total costs of carrying cost of Ordering.

19. Ordering costs
• The ordering costs are the costs that are incurred every
time an order for inventory is placed with the supplier.
• Examples of these costs include telephone charges,
delivery charges, invoice verification expenses and
payment processing expenses etc.
• The total ordering cost usually varies according to the
frequency of placing orders.
• Mostly, it is directly proportional to the number of
orders placed during the year which means If the
number of orders placed during the year increases, the
annual ordering cost will also increase and if, on the
other hand, the number of orders placed during the year
decreases, the annual ordering cost will also decrease.

20. Holding costs
• The holding costs (also known as carrying costs) are the
costs that are incurred to hold the inventory in a store or
warehouse.
• Examples of costs associated with holding of inventory
include occupancy of storage space, rent, shrinkage,
deterioration, obsolescence, insurance and property tax etc.
• The total holding cost usually depends upon the size of the
order placed for inventory. Mostly, the larger the order
size, the higher the annual holding cost and vice versa.
• The total holding cost is some time expressed as a
percentage of total investment in inventory.

21. Inventory Models - EOQ

22. Inventory Models – EOQ (without
shortage)
Exercise problems:
1. An electronic store sells 10,000 cell phones per year. Each
time an order is placed for a supply of cell phones, the
store incurs an order cost of Rs.10. The store pays Rs.100
for each cell phone and cost of holding a cell phone in
inventory for a year is assumed to be Rs.20. When the
store orders cell phones, how large an order should it
make?
2. An oil engine manufacturer purchases lubricants at the rate
of Rs. 42 per piece from a vendor. The requirements of
these lubricants are 1800 per year. What should be the
ordering quantity per order, if the cost per placement of an
order is Rs. 16 and inventory carrying charges per rupee
per year is 20 paise.

23. Inventory Models – EOQ (without
shortage)
Classwork problems:
1. The annual demand for an item is 3200 units. The unit cost
is Rs.6 and inventory carrying charges 25% per annum. If
the cost of one procurement is Rs.150, determine
Economic order quantity.
2. If the annual demand is Rs.6000 units, the storage cost is
Rs.0.60 per year per unit and the set up cost is Rs.80 per
run, find the optimum run size.
3. The material A is used uniformly throughout the year. The
data about annual requirement, ordering cost and holding cost
of this material is given below:
Annual requirement: 6000 units
Ordering cost: Rs.60 per order & Holding cost: Rs.2 per unit

24. 4. Calculate EOQ from the following?
Consumption during the year = 600 units
Ordering cost Rs. 12 per order
Carrying cost 20%
Selling Price per unit Rs. 20

25. Inventory Models – EOQ
Homework problems: (without shortage)
1. From the following data obtained in respect of an item of
store, calculate economic ordering quantity for item.
Total annual consumption – 12,000 units
Unit purchase price - Rs.1.00
Ordering cost - Rs.75.00 per order
Cost of carrying inventory - Rs.20% per annum
2. XYZ Ltd. consumes 4,000 units of a particular item every
year. The cost per order has been ascertained to be Rs.240.
The price of that unit is Rs.10 per unit. The inventory
carrying costs of the company are 30%. Determine EOQ.

26. Inventory Models – EOQ (with
shortage)
Exercise problems: (Manufacturing model)
1. A contractor has to supply 10,000 bearings per day to an
automobile manufacturer. He finds that, when he starts a
production run, he can produce 25000 bearings per day.
The cost of holding a bearing in stock for one year is 2
paise and the setup cost of a production run is Rs.18. how
frequently should produce run be made?
2. The demand for an item is a company is 18000 units per
year and the company can produce the item at a rate of
3000 units per month. The cost of one setup is Rs.500 and
the holding cost of one unit per month is 15 paise.
Determine the optimum manufacturing quantity.

27. Inventory Models – EOQ (with shortage)
Exercise problems: (Purchasing model)
1. A manufacturer has to supply his customer 24000 units of his
product per year. This demand is fixed and known. The
customer has no storage space and so the manufacturer has
to skip a days supply each day. If the manufacturer fails to
supply the penalty cost is Rs.0.20 per unit per month. The
inventory holding cost amounts to Rs.0.10 per unit per
month and the setup cost is Rs.350 per production run. Find
the optimum lot size for the manufacturer.
2. Demand of an item is uniform at a rate of 25 units per month.
The fixed cost is Rs.30 each time a production is made, the
production cost is Rs.2 per item and the inventory carrying
cost is 50 paise per unit per month. If the storage cost is Rs.3
per item per month. Determine how often to make a
production run and of what size?

28. Inventory Models – EOQ (with shortage)
Exercise problems:
3.Given the following data for an item of unit from demand,
instaneous delivery time and back order facility.
Annual Demand – 800 units
Cost of an item – Rs.40
Ordering Cost – Rs.800
Inventory carrying cost – 40%
Back order cost – Rs.10.
Find Minimum order quantity.

29. Inventory Models – EOQ
Homework problems: (with shortage)
1. Consider the following data:
Unit Cost – Rs.100
Order Cost – Rs.160
Inventory Carrying Cost – Rs.20
Backorder cost (Stock out cost) – Rs.10
Annual Demand – 1000 unit.
Find Minimum order quantity.
2. The demand for an item is uniform at a rate of 20 units per
month. The fixed cost is Rs.10 each time a production run is
made. The production cost is one rupee per item and the
inventory carrying cost is Rs.0.25 per item per month. If the
shortage cost is Rs.15 per item per year, determine how often
to make a production run and of what size it should be?

30. Inventory Models – EBQ
d is demand rate (daily rate)
P is production rate

31. Inventory Models – EBQ (without shortage)
Exercise problems: (without shortage)
1. M/S. KOBO Bearing Ltd. is committed to supply 24, 000
bearings per annum to M/S/ Deluxe fans on a steady daily
basis. It is estimated that it costs 10 paise as inventory
holding cost per bearing per month and the set up cost per
run of bearing manufacture of Rs.324.
2. Find the economic batch quantity from the following data:
Cost of carrying inventory – 15% of value per year
Set up cost – Rs.5000 per batch
Average yearly consumption – 3000 units
Cost per unit – Rs.100.

32. Inventory Models – EBQ (without shortage)
Classwork problems: (without shortage)
1. Find the economic batch quantity for manufacturing 20,000
fountain pens per year:
Value of raw material in each fountain pen – 2.00
Labour including on cost per fountain pen – 2.50
Set up cost per batch – Rs.600
Cost of carrying inventory – 12% of value per year.
2. The probability distribution of annual demand for cycles is
given below:
What is the economic manufacturing lot size, if the set up cost
is Rs.1000 per set up and the carrying cost is Rs.10 per cycle
per year.
Demand 3000 5000 10000 15000
Probability 0.1 0.3 0.5 0.1

33. Inventory Models – EBQ (without shortage)
Homework problems: (without shortage)
1. Determine the Economic batch quantity from the
following data:
Total sales in a year – 1500 units.
Set up cost per job order – Rs.1800
Cost of unit product - Rs.120
Inventory carrying charges – 10% of value of product.
2. Find the economic batch quantity from the following data:
Average annual demand – 30000 units
Inventory carrying cost – 12% of unit value per year
Cost of placing an order – Rs.70
Cost per unit – Rs.2

34. Inventory Models – EBQ (with shortage)
Exercise problems: (with shortage)
1. A positive moulding firm produces and uses 24000
teflon bearing inserts annually. The cost of setting
up of production is Rs.85 and the weekly
production rate is 1000 units. If the production cost
is Rs.5.50 per unit and the annual storage and
carrying cost is Rs.0.50 per unit, how many units
should the firm produce during each production
run?

35. Inventory Models – EBQ (with shortage)
Exercise problems: (with shortage)
2. A product is manufactured on a machine. The cost
of production, demand, etc., are given below:
Fixed cost per unit – Rs.30
Variable cost per unit – Rs.0.10
Percentage of charges for interest, taxes, insurance,
storage, etc. – 50%
Production rate 1,00,000 units per year
Demand rate 10,000 units per year
Determine the economic lot size manufacturing
quantity.

36. End of the Unit 5
Thank You