LESSON 5.1 SIMPLE AND COMPOUND INTEREST
SIMPLE INTEREST
Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Simple interest doesn't compound, which means a creditor will only pay interest on the principal
amount and a borrower would never have to pay more interest on the previously accumulated interest.
DEBTOR OR MAKER
The person who borrows money for any purpose
LENDER OR CREDITOR
The person or institution that loans the money
INTEREST
Is the payment for the use of borrowed money.
PRINCIPAL
The sum of money invested
INTEREST RATE
The fractional part of the principal that is paid on the loan and is usually express as percent.
TIME OR TERM OF THE LOAN
The length of time for which the money is borrowed.
FINAL AMOUNT OR MATURITY VALUE
The sum of the principal and the interest which is accumulated at a certain time.
TWO WAYS OF SIMPLE INTEREST
#Ordinary
#Exact
TWO WAYS OF FINDING TIME IN BETWEEN DATES
# Approximate
#Actual
ACCUMULATION
If interest is paid at the end of the term.
DISCOUNTING
If interest is paid at the beginning of the term.
-simple discount often called interest in advance.
PROCEEDS
The amount of the borrower receives.
FORMULA FOR SIMPLE AMOUNT AND SIMPLE INTEREST:
I=P*r*t where;
I= Interest
P= Principal amount (the amount of money borrowed)
r= rate (change the percent to decimal)
t= Time (in years) when the time is given in a months or days, it must be converted to years
F= Final amount
Alternately:
I= F-P
F=P+I
=P+Prt
=P(1+rt)
Other formulas:
P= I/rt
t= I/Pr years
P= F/1+rt
r=( I/pt)x100%
Example
Find the interest and the amount of P10,000 at 5 ½ % simple interest for 3 years.
Given:
P= P 10,000
t= 3 years
r= 3 ½% = 0.055
Required:
Interest (I)
Final amount (F)
Formula:
I= Prt
F= P+1
I= Prt
= (10,000)(0.055)(3)
I = 1,650
F= P+I
= 10,000+1,650
F=11,650
Alternate Solution
F= P(1 + rt )
=10,000(1+ 0.055 (3))
F= 11,650
COMPND INTEREST
Compound interest is the interest resulting from the periodic addition of simple interest to the capital
creating a new capital every now and then. In transactions covering an extended-period of time, interest
may be handled in different ways. Whenever at stipulated intervals, known as compounding or
conversion period, during the term of an investment or loan, the interest due is added to the principal
and thereafter earns an interest, the sum which represents the increase in the original principal at the
end of the term is called compound interest. The compound amount or the final amount is the sum of
the principal and the compound interest.
There are two types of interest rates used in the computation for investment earnings :
Effective rate - is the interest rate when interest is compounded once a year.
Nominal rate - is the interest rate when interest is compounded more than once a year.
Financial entities usually convert multiple loans of different rates into a loan that will equaily replace
the many loans either by single payment, equal payments or unequal payments.
Illustrative Examples:
1. Determine the final amount and the interest of P10,500 that is deposited savings account and is
invested at 10% compounded quarterly.
Given:
P P10,500
i = 0.10 = 0.025
t = 3 years = 10% = 0.10
m= 4
n = 3(4) = 12
Required:
Final amount (F)
Interest (I)
Formula:
F = P(1+i)^n
I = P [(1+1)^n - 1]
Computation:
F= P(1+i)^n
= P10,500 (1+0.025)12
=P14,121.33
I= P[(1+0)" - 1]
=P10,500 ((1+0.025)12 - 1]
=P 3,621.33
Alternative Solution :
I= F-P
=P14,121.33 - P10,500
= P 3,621.33
Thus, the compound amount of the savings deposit is P14,121.33 and the compound interest earned is
P3,621.33.