3 compound interest
DESCRIPTION
accTRANSCRIPT
Compound Interest
- computed every compounding period
and as such accumulates money more
rapidly
Compound Amount and Present Value
Interest Period – refers to the time between two
successive conversions
Frequency of conversion (m) – refers to the
number of conversions periods in one year
Nominal rate (r) – annual interest rate
Interest rate per period ( i ) :
Number of conversions during the term (n) :
ri
m
( )n t m
Time should always express in years.
Conversion periods used for compound interest
computation are:
Conversion Period
Frequency of
Conversion (m)
Annually 1
Semi - annually 2
Quarterly 4
Monthly 12
Compound Amount Formula:
To find the present value:
1n
F P i
1
1
n
n
FP or P F i
i
Examples:
1. Determine the compound amount if
P12, 000 is invested at 10%
compounded quarterly for 5 years.
2. Mr. Torres wants to have P150, 000 in his
account at the end of 10 years. How much
should he invest today in a bank that pays 8%
compounded monthly?
#2/23. A man invested P8500 for 4 years
at 6% converted annually. What is the
accumulated amount?
#3/23. How much is the interest and the
accumulated amount of P25,000
invested at 3 years at 4% converted
quarterly?
#7/24. The day the boy was born, his
father invested P20,000 at 6%
converted semi-annually. Find the
value at the boy’s 18th birthday?
Compound Amount at a Fraction of a Period
n is assume to be integer
1n
F P i
If n is a fraction, compound amount can
be compute by following the two steps:
1. Find the compound amount at the end
of the largest number of whole periods
in the given time.
2. Accumulate the result in Step1 for the
remaining time using simple interest.
Examples:
1. Find the compound amount if P5, 000 is
invested for 3 years and 9 months at 12%
compounded semi –annually.
2. Find the interest and amount of P1.5M if it is
invested from October 28, 1972 to November
28, 2005 at compounded quarterly.
110 %
2