NATURE OF DISCOUNT

The term “discount” as a noun, can mean any of the following:

1. Reduction from the full amount of a price or debt.
2. The interest deducted in advance in lending commercial paper.
3. The rate of interest deducted in a lending transaction.

As a verb, discount may connote the following:

1. To deduct from a price
2. To advance money after deducting interest
3. To reduce the value

Based on the different connotations given above, discount has no

precise and definite meaning. Basically, the meaning depends on
how it is used on a given context.
By the process of deduction, discount, therefore, refers to the
difference between two values and the present value of an
amount. We will use these two concepts of discount in the
succeeding discussions.

SIMPLE DISCOUNT
Simple discount refers to the difference between the future
value or amount due and its present value.
Simple discount is also equivalent to the simple interest. It is
called simple discount because the discount is computed only
once during the entire period of borrowing.
To facilitate easy discussion of simple discount, the terms
simple interest are place beside its equivalent terms in simple
discount.

Under Simple Interest Under Simple Discount

Principal = Present value
Maturity value or amount = Future value or amount due
Interest = Discount
Interest rate = Discount rate

Query: What is the salient difference between simple interest

and simple discount?
Answer: Under the concept of simple interest, the interest is
payable on the due date of the loan. In other words, the
borrower pays the creditor or the bank the principal amount plus
interest on the maturity date. Hence, the borrower receives the
full amount on that date.
In simple discount, the interest on the amount borrowed is
deducted in advance. In other words, the borrower receives only
the net amount (amount borrowed minus interest); and on the due
date, he/she will pay the principal in full.

Illustrative Problem 2.1.

Sol borrowed P15,000 at 12% for a term of 2 years.
Required: Determine the following under simple interest and
simple discount:
1. Interest deducted in advance
2. Amount received on the loan date
3. Amount payable on the due date
Answer and Analysis 1: The interest or discount on P15,000 at
12% for 2 years is computed as follows:
Interest/Discount = 15,000 x 12% x 2
= P3,600
In simple interest, the P3,600 is payable on the due date, while
in simple discount, the P3,600 is deducted during the loan date.
Hence, interest amount deducted in advance appear as follows:
Simple interest = 0 (not applicable)
Simple discount = P3,600
This means that if the borrowing is computed using the concept
of simple interest, no interest will be deducted in advance.
However, of the loan is made as a discount, the P3,600 interest
will be deducted in advance during the date of the borrowing.
Answer and Analysis 2: The amount received on loan date under
the two concepts is computed as follows:
Simple interest = P15,000
Simple discount = P11,400 (P15,000 – P3,600)
This means that on the loan date, the borrower will receive
P15,000 if the interest is computed based on the concept of
simple interest. On the other hand, if the loan is treated as a
discount, the borrower will receive P11,400 on the loan date.
Answer and Analysis 3: The amounts payable on the due date are
as follows:
Simple interest = P18,600 (P15,000 + P3,600)
Simple discount = P15,000
This means that if the interest is computed and treated under
the concept of simple interest, the borrower will pay P18,600 on
the due date. However, if the borrowing is considered as a
discount, the borrower will pay P15,000 upon the maturity
period.
In a tabular presentation, the above data appear as follows:
Simple Interest Simple Discount
Interest deducted in advance P0 P3,600
Amount received on the loan date P15,000 P11,400
Amount payable on the due date P18,600 P15,000
When the interest is deducted in advance, borrowing is
considered to be discounted.

Illustrative Problem 2.2.

Geraldine borrowed P20,000 at 12% discount rate, payable after 2
years and 6 months.
Required: Determine the discount.
Answer and Analysis: The discount is computed as follows:
Discount (D) = 20,000 x 12% x 2.5
= P6,000
On the loan date, Geraldine will receive P14,000 (P20,000-
P6,000), and will pay P20,000 on the due date. The P14,000 is
the present value, while the P20,000 is the maturity or future
value.

SIMPLE DISCOUNT FORMULAS

To compute for the discount, use:
D = Mrt
Where:
D = Discount
M = Maturity value
r = Discount rate
t = Discount time

To compute for the maturity value where the amount of discount

rate and time are given:
M = D /rt
To compute for the discount rate where the amount of discount,
maturity value, and time are given:
r = D/Mt
Finally, to compute for the discount time where the maturity
value, discount amount, and rate are given:
t = D/Mr

Illustrative Problem 2.3.

Find the maturity value of P4,500 discount interest for the
period of 8 months at 7.5%.
Answer and Analysis: the given values are:
D = P4,500
r = 7.5%
t = 8 months
M = ?

To solve for the maturity value:

M = D/rt
= 4,500 / 0.075 x 8/12
= P90,000

Illustrative Problem 2.4.

The discount interest is P1,300 on P65,000, discounted for 90
days. Find the discount rate.
Answer and Analysis: the given values are:
M = P65,000
D = P1,300
t = 90 days
r = ?

r = D/Mt
r = 1,300 / 65,000 x 90/360
= 0.08 or 8%

Illustrative Problem 2.5.

Find the discount time for P110,000 at 9.5% discount rate with
discount interest of P15,675.
Answer and Analysis: the given values are:
M = P110,000
D = P15,675
r = 9.5%
t = ?

to solve for the discount time:

t = D/Mr
t = 15,675 / 110,000 x 0.095
= 1.5 years

THE TERM “TO DISCOUNT” AND THE PRESENT VALUE

The term “to discount” means to determine the present value of
an amount. In other words, we are answering the query: what is
the value now (present value) of a certain amount payable at a
later period?
The formula to compute for maturity value by the process of
factoring is:
M = P (1 + RT)
Where:
M = Maturity value
P = Principal
R = Rate
T = Time

Maturity value refers to the sum of the principal and interest.

In other words, it is the future value of the principal at a
certain interest rate.
The principal in simple interest then, is equivalent to the
present value of maturity value or future amount.
In simple discount, the problem normally states the maturity
value. On the other hand, in simple interest computation, the
problem states the principal. The procedure applied to compute
the principal or present value is reversed when computing for
simple interest.
To solve for principal (P) in the above formula, divide both
sides of the equation by (1 + RT); hence:
𝑴 𝑷(𝟏 + 𝑹𝑻)
=
(𝟏 + 𝑹𝑻) (𝟏 + 𝑹𝑻)
Canceling (1 + RT) on the right of the equation, the formula to
compute the present value of simple discount appears as follows:
𝑀
𝑃 =
(1 + 𝑅𝑇)
İLLUSTRATIVE PROBLEM 2.6
On January 1, 2012, Joylyn discounted P24,750 at 9 1/2% for 2
years and 6 months.
Required: Find the present value of the amount.
Answer and analysis: The problem is asking us to determine the
present value of P24,750 which is the value by June 30, 2014,
that is, 2 years and 6 months from January 1, 2012.
The principal or present value is computed as follows:
𝑀
𝑃 = (1 + 𝑅𝑇)

24,750
= [1 +(0.095) 𝑥 2.5)]

= 24,750/1.2375
= P20,000
This means that the present value (value right now) of P24,750 –
the amount after after a period of 2 years and 6 months at 9.5%-
is P20,000.
In simple interest, the present value of the amount is equal to
its principal.

BANK DISCOUNT
Bank discount refers to the amount of interest deducted by the
bank in advance. The interest is computed based on the maturity
value of the loan. In other words, when the bank discounted a
loan, the borrower receives an amount less than what was
borrowed, since the interest has been deducted in advance.
Bank discount is computed as follows:
Bank discount = Maturity value x Discount rate x Time
The amount that the borrower receives is called proceeds. It is
the discounted value of the loan, and is computed as follows:
Proceeds = Maturity value – Bank discount

ILLUSTRATIVE PROBLEM 2.7

Jonard borrowed P50,000 from Community Bank at 12% discount rate
for 1 year and 6 months.
Required: Determine the bank discount and the proceeds of the
loan.
Answer and Analysis: The borrowed amount is discounted by the
bank; hence, the interest will be deducted in advance. The bank
discount is computed as follows:
Bank discount = 50,000 0.12 x 1.5
= P9,000
The P9,000 bank discount is deducted from the loan amount of
P50,000; hence, the proceeds of the loan are computed as
follows:
Proceeds = 50,000 - 9,000
= P41,000

As illustrated, the proceeds are determined by computing for the

discount first. However, by a factoring process, we can directly
determine the proceeds of the loan without computing for the
bank discount.
The formulas to compute the bank discount and proceeds are:
Bank Discount = Maturity value x Discount rate x Time
Proceeds = Maturity value - Bank discount

The following notations will be used:

B = Bank discount
M = Maturity value
d = Discount rate
T = Time
W = Proceeds
If we substitute the formula of the bank discount to the
proceeds formula, the expanded equation will appear as follows:
W = M - (M x d x T)
By the process of factoring, proceeds is computed as follows:
W = M [1 – (d x T)]
= M (1 - dT)
Applying the derived proceeds formula, the proceeds of the
P50,000 loan discounted at 12% for 1 year and 6 months are
computed as follows:
W = M (1 - dT)
= 50,000 [1 - (0.12 x 1.5)]
= 50,000 (1 -0.18)
= 50,000 (0.82)
= P41,000

DETERMINING THE AMOUNT OF LOAN TO BE DISCOUNTED

In Illustrative Problem 2.7, the loan amount is P50,000, and the
borrower receives only P 41,000 once the bank discounts the
loan.
Thus, if the total requirement of Jonard is P50,000 and the bank
discounted the loan, he is short by P9,000. Therefore, he should
borrow more than P50,000 to satisfy his total requirements.

Query: How shall we determine the desired loan amount or the

size of the loan to be discounted?
Answer: The size of the loan can be determined by working on the
proceeds formula.

Directly, the proceeds of the bank discount are determined by

the formula
W = M (1 - dT)

where:
W = Proceeds
M = Maturity value
d = Discount rate
T = Time
Bearing in mind that the maturity value is the final amount
payable on the due date of the loan, we can determine the
desired proceeds by the following process.
First, divide both sides of the equation by (1 – dT). Hence:
𝑾 𝑴(𝟏 − 𝒅𝑻)
=
(𝟏 − 𝒅𝑻) (𝟏 − 𝒅𝑻)
This cancels the (1 - dT) on the right side of the equation;
hence:
𝑾
𝑴=
(𝟏 − 𝒅𝑻)
The formula indicates that the size of the loan to be discounted
is equal to the maturity value.
ILLUSTRATIVE PROBLEM 2.8
Michelle needs P66,800 for an additional working capital. The
bank is charging a discount rate of 11% for are 1 year and 6
months borrowing.
Required: Determine how much should be loaned by Michelle.
Answer and Analysis: The desired amount is P66,800; hence, she
should borrow more than that amount. The amount to be borrowed
is computed as follows:
66,800
M (Desired amount) = [1−(0.11𝑥1.5)]

66,800
= (1−0.165)

66,800
=
0.835

= P80,000

Therefore, Michelle should apply for a loan of P80,000 in order

to satisfy her needed requirements of P66,800.

PROMISSORY NOTES
A promissory note is a written promise signed by the maker to
pay another person a certain sum of money in a fixed or
determinable future time.
The two types of promissory notes are:
1. Simple interest promissory note
2. Discounted interest promissory note
A promissory note may also be:
1. An interest-bearing note
2. A non-interest bearing note
The note is considered interest bearing when a certain interest
rate is specified on its face, while a non-interest bearing note
does not mention of any interest.
In a simple interest promissory note, the amount that appears on
the face of the note is the principal amount. The principal and
the interest comprise the total amount payable upon the maturity
date. In the discounted interest promissory note, however, the
amount that appears on the face of the note is the maturity
value of the loan.
An example of a simple interest promissory note may appear as
follows:
 P50,000 Davao City March 1, 2012

Ninety days after date, I promise to pay to the order

of Israel Mendoza Fifty Thousand Pesos for value received
with a 12% simple interest per annum.

Due: May 30, 2012 (Signed) Jiv Capo-an

The parts of a promissory note are as follows:

1. Maker – the person who signs and executes the note because of
borrowing. In the above note, Jiv Capao-an is the maker.
2. Payee – the person who extends credit or lends money. Israel
Mendoza is the payee.
3. Face value of the note - the principal or amount borrowed. In
the note, the face value is P50,000.
4. Date of the note - the date the note is made or signed. March
1, 2012 is the date of making or issuing the sample note.
5. Maturity date – the due date of the note. The note will
mature on May 30, 2012.
6. Term of the note - the length of time covered by the note. In
the example it is 90 days from March 1, 2012 to May 30, 2012.
If the sample promissory note is a discounted note, then P50,000
is equal to the maturity value of the loan. The borrower,
therefore, will receive proceeds less than face value of the
note.
The payee, in the promissory note, has the right to collect or
has a receivable from the maker. On the other hand, the maker
has the obligation to pay the face value of the note on the
maturity date.
A promissory note may be transferred from one person to another.
In transferring the note, the holder endorses it, and perfects
the transfer by delivery. A note that is transferred and
accepted by another person is called a negotiable promissory
note.
A non-interest bearing promissory note may appear as follows:
 P100,000 Davao City March 1, 2012

Ninety days after date, I promise to pay to the order of

Israel Mendoza Fifty Thousand Pesos for value received.

Due: May 30, 2012 (Signed) Jiv Capo-an

A non-interest bearing promissory note is basically the same in

appearance with an interest-bearing note, except that it does
not mention of any interest rate. Since no interest is imposed
for the loan amount, the maturity value of a non-interest
bearing note is equal to its principal.

DISCOUNTING OF AN INTEREST-BEARING PROMISSORY NOTE

Promissory notes arise because of credit. Usually, business
entities, banks, and persons - in order to increase their sales
or output - extend credit to customers’ sale products and
services on account. This type of transaction is usually
supported by promissory notes.

Discounting of a promissory note refers to the selling of the

note before its maturity date. It is one way for a business or
creditor to finance its receivable. When a promissory note is
discounted, the payee sells the note to the bank and receives
the proceeds at a discount. On the due date, the bank receives
the maturity value of the note, that is, the principal plus the
interest.
The following procedures may be observed in discounting a
promissory note:
1. Determine the maturity value of the note using the following
formula:
Maturity Value = Principal [1 + (Rate x Time)]
2. Determine the discount period. Discount period refers to the
remaining period from the date of discounting up to the maturity
date. In counting the remaining number of days or discount
period, always remember to exclude the first day but include the
last day.
3. Determine the discount using the following formula:
Discount (D) = Maturity value(M) x Discount rate(d) x Discount
period(t)
4. Determine the proceeds using the formula:
Proceeds (W) = Maturity value (M) – Discount (D)
ILLUSTRATIVE PROBLEM 2.9
On May 15, 2012, Golden Company received a P120,000, 90-day, 10%
simple interest-bearing note from its customer. The company
discounted the note on July 20, 2012 at Metro Pacific Bank at
12% discount rate.
Required: Determine the proceeds of the discounting.
Answer and Analysis: Applying the procedural steps indicated
above, the proceeds is computed as follows:
Step 1. Compute the maturity value:
M = P(1 + RT)
= 120,000 [1 + (10% x 90/360)]
= 120,000 (1 + 0.025)
= 120,000 (1.025)
= P123,000
Step 2. Compute the discount period:
Maturity date of note is August 13, 2012
(90 days from May 15, 2012) 90 days
Minus expired period (from May 15 to July 20) 66 days
Discount period 24 days

Step 3. Compute the discount:

D = M x d x t
= 123,000 x 12% x 24/360
= P984

Step 4. Compute the proceeds:

W = M – D
= 123,000 – 984
= 122,016

Therefore, on July 20, 2012, the period of discounting the

promissory note, Golden Company received P122,016 from Metro
Pacific Bank, the buyer of the note. On August 13, 2012, the
maturity period of the note, Metro Pacific Bank received from
the maker of the note P123,000.
DISCOUNTING OF A NON-INTEREST BEARING PROMISSORY NOTE
when a non-interest bearing note is discounted, the maturity
value is equal to its principal. In other words, there is no
need to compute for the maturity value; hence, the procedures
are less than 1 step from that of discounting an interest-
bearing note.

Illustrative Problem 2.10.

Lourdes borrowed P15,000 from Jean for a period of 8 months and
issued a non-interest bearing note. After 2 months, Jean sold
the note to Banco Negro at 12%.
Required: Determine the proceeds.
Answer and Analysis: the note issued by Lourdes is non-interest
bearing; hence, Jean will receive the amount borrowed on due
without interest. However, the payee sold the note at 12%
interest before its due date.
The discount is first computed as follows:
D = 15,000 x 12% x 6/12
= P900

To compute the proceeds:

W = 15,000 – 900
= P14,100

Or the proceeds may be directly computed using the formula:

W = M (1 – RT)
= 15,000 [1 – (12% x 0.5)]
= 15,000 (0.94)
= P14,100
In this case, Banco Negro paid Jean P14,100 on the discount
date, and the bank received P15,000 on the due date of the loan.

RELATIONSHIPS BETWEEN INTEREST RATE AND DISCOUNT RATE

In discounting promissory notes, there are two type of interest
that are used, namely the interest rate and the discount rate.
The interest rate is the rate that appears on the promissory
note; the discount rate is the rate used by the bank or the
buyer of the promissory notes. It is emphasized that interest
rate is different from discount rate. In case, however, that no
discount rate is provided, the interest rate is assumed to be
the discount rate.
Another difference between the two is that the interest rate is
used to compute the maturity value of the promissory note. The
maturity value is the full amount that the borrower will pay on
the due date. On the other hand, the discount rate is used to
determine the discount and proceeds of the discounting.
However, there is a similarity or direct relation between the
interest rate and the discount rate on either their future
values or present values. In the succeeding discussion, we will
evaluate their relationship based on present values.
Let us recall first the present value (the value now) formulas
of simple interest and simple discount.
The formula to compute the present value of an amount at simple
interest is:
P = M/ (1 + RT)
where:
P = Principal
M = Maturity value
R = Interest rate
T = Time

On the other hand, the formula to determine the present value of

a discount is:
D = M (1 - dT)

where:
D = Discount
M = Maturity value
d = Discount rate
T = Time
The interest rate (R) is equal to the discount rate (d), if the
present value of an amount at simple interest is equal to the
present value of a discount at simple discount rate.
The relationship is expressed as follows:
M/(1 + RT) = M(1 - dT)
If we divide both sides of the equation by M, we get:
1/(1 + RT) = (1 - dT)
Solving for R, we obtain:
R = d/(1 - dT)
Likewise, solving for d, we have:
d = R/(1+ RT)
From the above equation, relationships between the interest rate
and the discount rate have been determined as follows:
R = d/(1-dT) and d = R/(1+RT)

The relations depicted in the equation above do not mean that

interest rate is equal to discount rate. Neither do they mean
that the interest rate will give the same amount if discounted.
Rather, we can determine the discount rate that is equivalent to
the simple interest or the other way around.
In other words, we are trying to answer this query: What
interest rate equivalent to the discount rate at the present
value of an amount?

ILLUSTRATIVE PROBLEM 2.11

Nelly wants to know what interest rate is equivalent to a 10%
discount rate if discounted for 1 year and 6 months. She plans
to extend a loan with a maturity value of P10,000.
Answer and analysis: The problem is asking to determine what
interest rate is equal to a 10% discount rate for a period of 1
year and 6 months.
In this case:
Discount rate = 10%
Time = 1 year and 6 months or 1.5 years

The equivalent interest rate is computed as follows:

R = d/(1-dT)
= 0.10/[1-(0.10 x1.5)]
= 0.117647 or 11.7647%
This means that a simple interest of 11.7647% is equal to 10%
discount rate for a period of 1 year and 6 months.
Assuming that the future amount is R10,000, let us prove that
the two rates are equal based on their present values.
The present value of P10,000 at 11.7647% simple interest for a
period of 1 year and 6 months is computed as follows:
P = M/(1 + RT)
= 10,000/[1 + (0.117647 x 1.5)]
= 10,000/(1.1764705)
 = P8,500

On the other hand, the present value of P10,000 at a discount

rate of 10% for a term of 1 year and 6 months is as follows:
D = M (1 - dT)
= 10,000[1 - (10% x 1.5)]
= 10,000 (0.85)
= P8,500
Obviously, the simple interest rate of 11.7647% is equal to 10%
discount rate for a term of 1 year and 6 months, since they give
the same present value of P8,500 on the P10,000 future amount.
It can be deduced then from the discussion that the same or
equal simple interest and discount rates for a certain period
will not produce equal discounted values. A simple interest rate
of 15% is not equal to a discount rate of 15%.

ILLUSTRATIVE PROBLEM 2.12

Annie wants to know the discounted value of P10,000 after 1 year
and 6 months at the following rates:
1. 10% simple interest rate
2. 10% discount rate
Answer and analysis 1: Again, the phrase "to discount” means to
determine the present value; hence, the amount given is a
maturity value or future value.
The discounted value of P10,000 at 10% simple interest rate for
1 year and 6 months is computed as follows:
P = M/(1 + RT)
= 10,000/[1 + (10% x 1.5)]
= 10,000/1.15
= P8,695.65

Answer and analysis 2: On the other hand, the discounted value

of P10,000 at 10% discount rate for the term 1 year and 6 months
is computed as follows:
D = M (1 - dT)
= 10,000 [1 - (10% x 1.5)]
= 10,000 (0.85)
= P8,500
It can be observed that the discounted value of a simple
interest rate is higher than the discounted value of a discount
rate, since in simple interest, the future value or maturity
value is higher than the principal. Usually, the principal
appears as the face value of a simple interest note.
Basically, in a simple interest note, the borrower receives the
full face value of the amount appearing on the notes; while in a
discounted note, the borrower receives only the proceeds.
Generally, the proceeds are lower than the maturity value.

EFFECTIVE RATE OF INTEREST

Effective rate of interest refers to the true or real interest.
It is measured based on the ratio of interest or discount over
the sum of the proceeds of the borrowings and their terms.
In a simple interest note, the nominal rate is likewise
considered as the true or effective interest, since the borrower
receives the full amount of borrowings. In other words, the
proceeds of the loan are equal to the principal.
Whereas in a discounted interest note, the borrower receives
only the proceeds, that is, the difference between the maturity
value and the discount. The proceeds are basically lower than
the face value; hence, the interest in a discounted note is not
the true or effective interest rate.
The formulas to compute the effective interest rate are as
follows:
For simple interest note:
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
Effective interest rate =
𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑇𝑖𝑚𝑒

For discounted interest note:

𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡
Effective interest rate = 𝑃𝑟𝑜𝑐𝑒𝑒𝑑𝑠 𝑥 𝑇𝑖𝑚𝑒

ILLUSTRATIVE PROBLEM 2.13

Ruthie plans to borrow P50,000 from City Bank for a period of 2
years and 6 months at 12% simple interest per year.
Required: Determine the effective interest of the loan if Ruthie
issues a:
1. Simple interest promissory note
2. Discounted interest promissory note
Answer and analysis 1: In a simple interest promissory note, the
amount appears on the face of the note is the principal amount
the borrower receives on loan date.
The interest is first determined as follows:
Interest = 50,000 12% x 2.5
= P15,000

Then, the effective rate of interest is determined as follows:

Effective interest rate = 15,000/(50,000 x 2.5)
= 15,000/125,000
= 0.12 or 12%
As shown in the above illustrative problem, in a simple interest
note, the interest that appears on the face of the note is also
the effective interest rate.

Answer and analysis 2: The amount that appears on a discounted

interest promissory note is the maturity value of the note. This
is the amount payable on the due date. Since the note is
discounted or the interest has been deducted in advance, the
borrower, therefore, receives an amount lower than the face
value.
The discount is first determined as follows:
Discount = 50,000 x 12% x 2.5
= P15,000
The discount will then be deducted from the maturity value to
computer proceeds, hence:
Proceeds = 50,000 - 15,000
= P35,000

Or we can immediately compute the proceeds using the formula:

Proceeds = Maturity value (1 - RT)
= 50,000 [1 - (12% x 2.5)]
= 50,000 (1 - 0.3)
= 50,000 (0.70)
= P35,000
If we compute proceeds using this formula, then the discount is
the difference between the maturity value and proceeds.
The effective interest rate is now computed as follows:
𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡
Effective interest rate = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑇𝑖𝑚𝑒

15,000
= 35,000 𝑥 2.5
 = 15,000 87,500
= 0.1714 or 17.14%
Based on the computation made, the effective interest rate of a
discounted interest- bearing note is 17.14%. The 12% interest on
the borrowing is only a nominal interest rate.
In commercial practice, the borrower usually pays the bank
processing fee, application fee, attorney's fee, and other
similar charges in addition to the interest when applying for a
loan. The additional charges imposed by the bank should be added
to the interest or discount to determine the effective interest
or real interest rate charged by the bank.

PARTIAL PAYMENT OF NOTES

A simple interest promissory note is sometimes settled by the
maker or holder through a series of partial payments instead of
a single payment upon reaching the maturity date. In other
words, the whole amount due (maturity value) is settled by a
series of payments up to the due date.
Usually, the problem encountered in this case is the
determination of the required payment to settle the whole
obligation on the due date.

These steps may be observed:

1. Compute the maturity value with the entire terms of the
borrowing. This is the sum of all partial payments and the final
payment on the due date. In other words, the sum of all partial
payments and the final payment should not be more than the sum
of the principal and the interest;
2. Deduct from the maturity value all partial payments made and
unexpired interest applicable to partial payments. The unexpired
interest applicable to partial payment is counted from partial
payment date up to the due date; and
3. The difference between the maturity value (Step 1) and all
partial payments, including the unexpired interest (Step 2), is
equal to the balance on the due date.

ILLUSTRATIVE PROBLEM 2.14

Filma borrowed P30,000 at 12% simple interest per annum payable
after 1 year. 4 months thereafter, she paid P6,000 and made
another partial payment of $8,000 after 10 months.
Required: Determine the amount due on maturity date.
Answer and analysis: The borrowing is at simple interest, but
before the due date, the debtor made a series of partial
payments.
Applying the steps indicated above, the amount due on the
maturity date is computed as follows:
Maturity value 30,000 (1 + (12% 1)] 33,600
Less: Payments and unexpired interest
1st partial payment P6,000
Unexpired interest for the 8 remaining months
(6,000 12% * 8/12) 480
2nd partial payment 8,000
Unexpired interest for the 2 remaining months
(8,000 12% * 2/12) 160 14,640
Amount due on maturity date P18,900

The maturity value of the borrowing is computed only once, since

the interest charged is a simple interest.