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Simple Interest
Basic terms
Interest
–
an amount charged for the use of money
Principal
–
the amount of money borrowed
Term
–
the length of the transaction period; it starts on the
srcin date
and ends on the
maturity date
Maturity value
–
the amount of money received at the end of the term; the sum of the principal and the interest earned. Also known as
Future Value
.
Simple interest
–
a type of interest wherein only the srcinal principal earns interest for the duration of the term
Formula for simple interest
Example.
Find the interest earned after 3 years if Php12,000 is deposited in a savings account which earns 5% simple interest.
Formula for the maturity value
F
:
F = P + Is
ã
F
is a future value, received at the end of the term. In this context, we say that the principal
P
is the current or present value of
F
.
Example.
What is the maturity value of an 8,000-peso debt payable in 2 years at 12.75% simple interest? What is amount of interest?
Derived formulas: Example:
A 5-year investment had a maturity value of Php27,500. If the applied rate was 7.5% simple interest, what was the srcinal principal?
Example:
At what simple interest rate was Php16,500 invested if it earned an interest of Php1,620 just after 1.5 years?
Example:
How long will it take a Php30,000 debt to earn an interest of Php4,500 if the simple interest being charged is 9%?
All about time
ã
In number of months
ã
In number of days
Ordinary Interest: Exact Interest:
▫
Note:
Default is Ordinary interest
▫
Note:
Default is Ordinary interest
ã
In between two dates
Actual time
–
count the actual number of
days of each month ▫ Approximate time –
assume each month has 30 days
Example:
the term is from February 2 to May 21, 2015.
▫
Ordinary Interest, approx. time:
= 109 360 Ordinary Interest, actual time:
= 108 360
▫
Exact Interest, approx. time:
= 109 365
▫
Exact Interest, actual time:
= 108 365
All about time
ã
In between two coinciding dates
▫ Count the number of months
▫ From March
21,
2016 to July
21
, 2016, there are 4 months. Thus,
=4 12
ã
Note:
if
t
is not whole number or exact decimal, express in
fraction.
e.g.
if the term is 5 months, write t = 5 NOT 0.42 12
Example.
Accumulate Php14,500 at 6.25% simple interest for 1 year and 6 months. (
To accumulate means to find the maturity value.)
Example.
Find the present value of Php100,000, which is due in 200 days, if money's worth is 10.5% simple interest.
Example.
Find the maturity value of a 150,000-peso investment from May 24, 2011 to January 12, 2012 at 7.25% simple interest. There are 233 days between the two dates.
Example.
Find the maturity value of a 50,000-peso debt at 8.15% from May 24, 2011 to January 24, 2012.
Example.
Melba lends Php50,000 to Jane on October 1, 2010 at 9% simple interest. Jane promised to fully settle the debt on March 28, 2011. Find the amount Melba will receive on the maturity date using:
a. Ordinary interest; actual time b. Ordinary interest; approximate time c. Exact interest; actual time d. Exact interest; approximate time

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