MATHEMATICS
OF FINANCE
Simple Interest
Definition of terms (Fajardo,2000) :
In business transactions, interest may be defined in
tw o different w ays.
To investor; interest is an
income derived from invested capital.
To debtor; interest is
money paid as rental for the use of
money.
Interest (I)
-is a fixed rated
proportion as the rate of
interest for any
specified time unit.
Interest rate (r)
-the ratio of the interest
earned one time unit to
the principal.
©https://www.firstcircle.ph/blog/compare-business-loan-interest-rates
Interest rate (r) is the
measure of the interest on
one peso for one time unit.
Principal (P) refers to the
capital originally invested
in a business transaction.
Full Amount (F) is the sum
of the Principal and the
Interest due at any time
after the investment of the
principal.
Illustration:Find the simple interest and the full
amount on P3,000 at 5% interest for two years.
Solution:
1.
Using the formula, I=Prt , substitute;
I= P 3,000 x 0.05 x 2 years
I = P 300.00
2. F= P + I
F= 3,000 + 300.00
F= P 3,300
Illustration: Find the value of Principal P and the Full Amount
F if the investment earns Php 200 in 18 months at the rate of 8%.
Solution:
Illustration: Find the value of Principal P and the Full Amount
F if the investment earns Php 200 in 18 months at the rate of 8%.
Solution:
Illustration: If 500 is the interest earned of 8,000 which was
invested for 16 months, 𝑰how much is the rate of interest?
𝑰
Using
formula
Using
thethe
formula
r =r =𝑰
𝑰
𝑷𝒕 r =
Using the formula
r = 𝑷𝒕
Solution:
Using the
formula
𝑷𝒕
𝑷𝒕
𝟓𝟎𝟎 𝟓𝟎𝟎
𝟓𝟎𝟎
r =r = 𝟓𝟎𝟎 r𝟏𝟔= 𝟏𝟔
𝟏𝟔
r =(𝟖,𝟎𝟎𝟎)(
(𝟖,𝟎𝟎𝟎)(
)
𝟏𝟔)(𝟖,𝟎𝟎𝟎)(
)
𝟏𝟐
𝟏𝟐
𝟏𝟐
(𝟖,𝟎𝟎𝟎)( )
𝟏𝟐
𝟓𝟎𝟎
𝟓𝟎𝟎r = 𝟓𝟎𝟎
r =r = 𝟓𝟎𝟎 𝟏𝟎,𝟔𝟔𝟔.𝟔
r =𝟏𝟎,𝟔𝟔𝟔.𝟔
𝟏𝟎,𝟔𝟔𝟔.𝟔
𝟏𝟎,𝟔𝟔𝟔.𝟔r = 0.0468 or 4.68%
r =r0.0468
or or
4.68%
= 0.0468
4.68%
r = 0.0468 or 4.68%
Seatwork:
1. If 5,000 earns Php86.00 interest in 15 months, how much is the rate
of interest?
2. If the interest rate is 7.5% per year and the principal is Php2,500,
determine the amount of interest for 20 months including the full
amount.
3. How long will it take to accumulate Php3,200 to Php4,800 if money
is worth 6.5%?
4. At what simple interest rate is Php20,500 the interest for 12 years
on 40,000?
5. Mr. Cruz agreed to pay Mr. Toledo Php100,000 at the end of 5
years. How much should Mr. Cruz pay now to settle his account if
Mr. Toledo agrees that money is worth (a) 8 -1/2% simple interest ,
(b) 9-1/2% simple interest ? Which rate is advantageous for Mr.
Cruz and for Mr. Toledo?