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Title: Math Study Guide: Simple Interest and Simple Discount
Description: In this study guide, all about Simple Interest and Simple Discount topics will be discuss such as: -final value / maturity value - ordinary and exact interest - actual time and approximate time - ordinary interest for actual and approximate time - exact interest for actual and approximate time - accumulation and discount at simple interest - discounting an interest bearing note before maturity - discounting a non interest bearing note before maturity There are also examples such as problem solving provided on every topic. Very clear, easy and understandable. I assure you this will help you understand more about Simple Interest and Simple Discount.

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SIMPLE INTEREST
→ SIMPLE INTEREST:
- deposited money in bank
- bank may lend the deposited money (loans)
- borrowing money from a bank

BASIC CONCEPTS:
LENDER

BORROWER

- lending the money or extending credit

- lending money/credit

- earns income from borrower

- pays interest to lender

- examples: loan, loan sharks, pawnshop, banks,
and lending institution

SIMPLE INTEREST

COMPOUND INTEREST

- original principal bears interest for the entire
term of a loan

- principal and interest earn interest also

Interest:
- amount paid for the use of money or the price paid for the use of credit
...


SIMPLE INTEREST FORMULA:

I = (P)(r)(t)

EXAMPLE:
1
...
5% simple interest for 2 years
...
5% (6
...
065
t = 2 years

Solution:
I = (P)(r)(t)
= (5000)(0
...

P= I
——
(r)(t)

→ amount (loan/investment)

EXAMPLE:
1
...
25 interest after 9 months
...
What was the
principal?
Find:

P (Principal) = ?

Given:

I = $11
...
05
t = 9 months

Solution:
P= I
——
(r)(t)
P = 11
...
05)(9/12)
P = 11
...
0375
Answer: P = $300


Interest Rate (r) - the ratio of the interest in one unit of time
...


Dora invested $30,000 in the stock market which guaranteed an interest of $5,600 after 3
years
...
0622
Answer: r = 6
...

t= I
——
(P)(r)

→ term of the loan

EXAMPLE:
1
...
If she paid $14,500
at the end of the specified term, how long did she use the money?
Find:

t (time) = ?

Given:

P = $10,000
I = (repaid 14,500) - (loan 10,000) = $4,500
r = 12% (12 / 100) = 0
...
12)

t=

4500
—————
1200

t = 3
...
75)(12 yrs) = 9 months
Answer: 3 years and 9 months

→ FINAL VALUE / MATURITY VALUE:
- sum of the principal and interest which is accumulated at a certain time
...

FORMULA:
F= P+I
F = P + Prt
F = P [1+ (r)(t)]
- when use for loan, F is the total amount to be repaid to the lender; this sum is called
MATURITY VALUE of the loan
...
The sum is called the FUTURE
VALUE of the investment
...


Calculate the maturity value of a simple interest, 8 month loan of $80,000 if the interest rate is
9
...

Find:

F=?

Given:

P = $80,000
r = 9
...
75 / 100) = 0
...
0975)(8/12)]
(80000)(1
...


Ordinary Interest
- where the year is taken as 360 days
...


Io = Pr (D / 360)

Exact Interest
- where the year is taken as 365 days
...


Invest in $50,000 at 5% simple interest for 45 days
...

Find:

Io = ?
Ie = ?

Given:
P = $50,000
r = 5% (5 / 100) = 0
...
05)(45/360)
Io = $312
...
05)(45/365)
Ie = $308
...
5
Ie = $308
...


Actual time
- exact/actual number of days in any given month
...

- 30 days: April, June, September and November
...


2
...


EXAMPLES:
1
...

Solution:

MONTH
April → from 21st to end of month
May → full month
June → full month
July → full month
August → full month
September → full month
October → from 1st to 24th
Answer:

2
...

Solution:

MONTH
November → from 1st to end of month
December → full month
January → full month
February → full month
March → from 1st to 23rd
Answer:

ACTUAL # OF DAYS
29
31
31
28
23
142 days

APPROXIMATE # OF DAYS
29
30
30
30
23
142 days

→ INTEREST BETWEEN DATES:
* 4 VARIETIES OF INTEREST:
1
...

3
...


Ordinary Interest for Actual
Ordinary Interest for Approximate
Exact Interest for Actual
Exact Interest for Approximate

EXAMPLE:
1
...

Find:

D (actual and approx
...
05

Solution:
MONTH
April → from 21st to end of month
May → full month
June → full month
July → full month
August → full month
September → full month
October → from 1st to 24th
1
...


Io = Pr (D / 360)
Io = (50000)(0
...
67
3
...
05)(186/365)
Ie = 1273
...
67
Io (for approx) = 1270
...
97
Ie (for approx) = 1253
...
05)(183/360)
Io = 1270
...


Exact Interest for Approximate
Ie = Pr (D / 365)
Ie = (50000)(0
...
42

2
...
5% from November 1, 2018
to March 23, 2019
...
5% (6
...
065

Solution:
MONTH
November → from 1st to end of month
December → full month
January → full month
February → full month
March → from 1st to 23rd
Ie = Pr (D / 365)
Ie = (6025)(0
...
36
Answer: Ie = 152
...
36

ACTUAL # OF DAYS
29
31
31
28
23
142 days

APPROXIMATE # OF DAYS
29
30
30
30
23
142 days
F=P+I
F = 6,025 + 152
...
36

3
...
Hardgiver borrows $60,000 from Mr
...
What amount
does Mr
...
09

Solution:
MONTH
May → from 26th to end of month
June → full month
July → full month
August → full month
September → full month
October → full month
November → from 1st to 6th

ACTUAL # OF DAYS
5
30
31
31
30
31
6
164 days

Io = Pr (D / 360)
Io = (60000)(0
...

- it is used for diagramming problems involving multiple payments or investments
...

→ NATURE OF DISCOUNT
Discount (noun):
- reduction from the full amount of a price or debt
...

- the rate of interest in a lending transaction
...

- to advance money after deducting interest
...

NOTE:
→ to accumulate is to find the amount, F
...


EXAMPLES:
1
...

Find:

F=?

Given:

P = $10,000
r = 7% (7 / 100) = 0
...
07)(3)]
(10000)(1
...


Discount $20,000 for 8 months at 9% simple interest
...
09
t = 8 months

Solution:
P=

F
————
1 + (r)(t)

P=

20000
—————
1 + (0
...
92
P = 20,000 - 18,867
...


P = 1,132
...

Find:

r=?

Given:

P = $100,000
F = $122,500
t = 3 years
Another Solution:

Solution:
F = P [1+ (r)(t)]
122,500 = 100,000 [1 + (r)(3)]
122,500 = 100,000 [1 + (r)(3)]
——— = ————————
100,000
100,000
1
...
225 -1 = 3r
0
...
225
3r
—— = ——
3
3
r = 0
...
5%

I = 122,500 - 100,000
= 22,500
r= I
——
(P)(t)
r = 22,500
————
(100,000)(3)
r = 22,500
————
300,000
r = 0
...
5%

SIMPLE DISCOUNT
→ SIMPLE DISCOUNT:
- when individuals borrow money and interest is charged for the use of money
...

→ BANK DISCOUNT:
- amount of interest deducted by the bank in advance
...

FORMULA: I = (F)(d)(t)



The amount that the borrower receives is called PROCEEDS
...




To facilitate easy discussion of simple discount, the terms in simple interest is placed
beside its equivalent terms in simple discount
...


Hyzel borrowed $230,000 at 8¾% bank discount rate for 1 year and 9 months
...

Find:

P (Proceeds/Present Value) = ?
F (Maturity value) = ?

Given:

money borrowed = $230,000
d = 8¾% (3/4 = 0
...
75% (8
...
0875
t = 1 year and 9 months (9/12 = 0
...
75

Solution:
a
...
75)
d = 8
...
75 / 100) = 0
...


Solve for t:
t = 1 year and 9 months (9/12 = 0
...
75

c
...
0875)(1
...
25

d
...
25
———————
1 - (0
...
75)

F=

194,781
...
153125

F=

194,781
...
846875

F = $230,000
Answer: P = $194,781
...


Find the amount due at the end of 8 months whose present value is $80,000:
a
...
09
t = 8 months

Solution:
F=

P
————
1 - (d)(t)

F=

80,000
——————
1 - (0
...
06

F = 80,000
———
0
...
38
b
...
09
t = 8 months

Solution:
F=
F=
F=
F=

P [1+ (r)(t)]
80,000 [1+ (0
...
06)
$84,800

Answer: F = $84,800

NOTE:


Two rates are equivalent if for the same present value (P), they yield the same maturity
value (F), at the end of the earn
...


What simple interest rate is equivalent to the simple discount rate 6% in discounting an
amount for:
a
...


6 months:

Find:

r=?

Find:

r=?

Given:

d = 6% (6 / 100) = 0
...
06
t = 6 months

Solution:

Solution:
r=

d
————
1 - (d)(t)

r=

d
————
1 - (d)(t)

r=

0
...
06)(3/12)

r=

0
...
06)(6/12)

Answer: r = 0
...
09%
2
...
0618 or 6
...

Find:

d=?

Given:

r = 5% (5 / 100) = 0
...
05
—————
1 + (0
...
0487 or 4
...

→ DISCOUNT: the interest that banks deduct in advance
...

→ PROCEEDS: the amount the borrower receives after the bank deducts its discount from the
loans maturity value
...

→ DISCOUNTING AN INTEREST-BEARING NOTE BEFORE MATURITY:
EXAMPLE:
1
...
A banker discounts this note for Robin Sun
at 9% on August 14, 2017
...


Find the maturity date and maturity value:
Given:

P = $200,000 ;

r = 7% (7 / 100) = 0
...
07)(150/360)]
F = $205,833
...
33
b
...
14, 2017 to Dec
...
33

;

d = 9% (9 / 100) = 0
...
33

P = F [1 - (d)(t)]
P = 205,833
...
09)(120/360)]
P = $199,658
...


On July 16, 2017 Gibson draws a note to the order of Johnson promising to pay $120,000
without interest at the end of 3 months discounted on September 1, 2017 at 9%
...


Find the term of discount (# of days from Sept
...
16, 2017) and proceeds:
Given:

F = $120,000
r = 9% (9 / 100) = 0
...
09)(45/360)]
P = $118,650
Answer: TERM OF DISCOUNT = 45 days
PROCEEDS = $118,650


Title: Math Study Guide: Simple Interest and Simple Discount
Description: In this study guide, all about Simple Interest and Simple Discount topics will be discuss such as: -final value / maturity value - ordinary and exact interest - actual time and approximate time - ordinary interest for actual and approximate time - exact interest for actual and approximate time - accumulation and discount at simple interest - discounting an interest bearing note before maturity - discounting a non interest bearing note before maturity There are also examples such as problem solving provided on every topic. Very clear, easy and understandable. I assure you this will help you understand more about Simple Interest and Simple Discount.