1 1 simple-interest

1.1 Simple Interest1.1 Simple Interest

Simple Interest


• 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 origin 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


Origin date Maturity date

Term

Principal Maturity value


• Simple interest – a type of interest wherein only the original principal earns interest for the duration of the term

• Formula for simple interest IS :

€

IS = Prt

€

P - principal (in any currency)

r - rate per year (in decimal form)

t - term (in years)


Example. Find the interest earned after 3 years if Php12,000 is deposited in a savings account which earns 5% simple interest.

€

Is = Prt

€

=(12,000)(.05)(3)

€

=Php1,800


• Formula for the maturity value F:

• 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.€

F = P + Is

€

or F = P(1+ rt)


Example. What is the maturity value of an 8,000-peso debt payable in 2 years at 12 ¾% simple interest?

€

F = P(1+ rt)

€

=8,000[1+ (.1275)(2)]

€

=Php10,040


Derived formulas:

€

P =Isrt

€

r =IsPt

€

t =IsPr

€

P =F

1+ rt


Example: A 5-year investment had a maturity value of Php27,500. If the applied rate was 7.5% simple interest, what was the original principal?

€

P =F

1+ rt

€

=27,500

1+ (.075)(5)

€

=Php20,000


Example: At what simple interest rate was Php16,500 invested if it earned an interest of Php1,620 just after 1.5 years?

€

r =IsPt

€

=1,620

(16,500)(1.5)

€

=.0655

€

=6.55%


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%?

€

t =IsPr

€

=4,500

(30,000)(.09)

€

=1.67 years


All About Time

€

t = 39 months

€

⇒ t = 3912

€

t =150 days

€

⇒ t = 150360

€

t is from March 21, 2011 and July 14, 2011

€

⇒ t = actual or approximate time360 or 365

€

⇒ t = 150365

€

t is between two dates which coincide

€

⇒ t = no. of months12


Example. How much is the maturity value if Php14,500 is placed in an account earning 6.25% simple interest for 18 months?

€

F = P(1+ rt)

€

=14,500 1+ (.0625) 1812( )[ ]

€

=Php15,859.38


Example. Find the present value of Php100,000, which is an amount due in 200 days, if money's worth is 10.5% simple interest.

€

P =F

1+ rt

€

=100,000

1+ (.105) 200360( )

€

=Php94,488.19


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.

€

F = P(1+ rt)

€

=150,000 1+ (.0725) 233360( )[ ]

€

=Php157,038.54


Example. Find the maturity value of a 50,000-peso debt at 8.15% from May 24, 2011 to January 24, 2012.

€

F = P(1+ rt)

€

=50,000 1+ (.0815) 812( )[ ]

€

=Php52,716.67


1. Given P = Php12,500, r = 10%, t = 3.5 years, find Is.

€

Is = Prt

€

=(12,500)(.10)(3.5)

€

=Php4,375


3. Given P = Php34,600, r = 12 ¼ %, t = 7 years and 3 months, find F.

€

F = P(1+ rt)

€

=34,600 1+ (.1225) 7 312( )[ ]

€

=Php65,329.13


5. Given F = Php37,450, r = 8.3%, t = 6 years, find P.

€

P =F

1+ rt

€

=37,450

1+ (.083)(6)

€

=Php25,000


7. Given P = Php36,000, Is = Php30,240, t = 7 years, find r.

€

r =IsPt

€

=30,240

(36,000)(7)

€

=12%


9. Given P = Php350,000, Is = Php257,250, r = 10.5%, find t.

€

t =IsPr

€

=257,250

(350,000)(.105)

€

=7 years


13. Susan lends Php50,000 to Jane on October 1, 2010. She expects Jane to pay the principal and simple interest at 9% to fully settle the debt on March 28, 2011. What amount does Susan receive?

€

F = P(1+ rt)

€

=50,000 1+ (.09) 178360( )[ ]

€

=Php52,225


15. Find the principal which will amount to Php3,066,000 in 3 years at 9.25% simple interest rate.

€

P =F

1+ rt

€

=3,066,000

1+ (.0925)(3)

€

=Php2.4M


17. Accumulate Php85,000 for 20 months at a simple interest rate of 12%.

(Note: To accumulate an amount means to find its maturity value.)

€

F = P(1+ rt)

€

=85,000 1+ (.12) 2012( )[ ]

€

=Php102,000


19. At what simple interest rate will Php415,000 increase to Php500,000 in 3 years?

€

r =F − P

Pt

€

=500,000 − 415,000

(415,000)(3)

€

=6.83%


21. When will Php42,000 increase to Php50,000 if the simple interest rate at which it is invested is 11.4%?

€

t =F − P

Pr

€

=50,000 − 42,000

(42,000)(.114)

€

=1.67 years


27. In what time will Php5,000 double itself at the rate of 9% simple interest?

€

t =F − P

Pr

€

=10,000 − 5,000

(5,000)(.09)

€

=11.11 years

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