# MATA32H3 Study Guide - Final Guide: Logarithm, Net Present Value, Integral

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School
Department
Course

MATA 32- Calculus for
Management I
Final Exam Study Guide
University of Toronto (UTSC) β Fall 2015
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MATA32 β Lecture #1: Compound Interest
Compound Interest
Deals with money, time and interest
1 key equation:
π=π(1+π)!
P ! Principle
β’ Money invested now
r ! Periodic interest rate
β’ Interest paid per compounding period
β’ Stated in percentage or annual rate
o NOTE: Must convert percentage into a decimal
n ! Number of compounding periods
β’ Counts number of times interest is paid on investment
S ! Compound Amount
β’ Amount of money we have at the end
Interest is paid exactly at the end of compounding periods
β’ Only at the end of compounds
**For one compound period, the principle (P) plus the interest on that
1st Compound ! π1+Pr =!π!(1+π)
2nd Compound ! π!1+π+!π!1+πβπ=π!1+π1+π=π!(1+π)!
3rd Compound ! π!(1+π)!+!π!1+πβ!π=!π!1+π!β!1+π=π!(1+π)!
4th Compound ! π!(1+π)!
NOTE: IN APPLICATIONS
β’ We often have APR βaβ (Annual Percentage Rate) and frequency βkβ of
compounding; and
o How often interest is paid in a year
β’ A time βtβ period
!
!
!
!
!
!
Khl!
Compounding periods
End
Start
Fixed Period of time
n!
P \$
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Legend:
a ! APR for period as follows
k ! Compounding frequency per year (annually)
t ! Number of years for a particular period
We have thatβ¦
!
!= r and π=πβπ‘
Thus,
π=π!(1+!
π
π)!β!
Example 1: Consider the following βinvestment schemeβ invest \$10,000 at 3.05% APR
compounding monthly for a period of 5 years.
a) Find compound amount
π=10,000!1+!.!"!#
!"
!"
β11,645.17
b) Periodic rate (interest at the end of each month)
π=
π
π
=
0.0305
12
β0.002542!(0.2542%)
c) Compound Interest
Difference between beginning amount and end amount
πβπ!
β1,645.17
Return due to interest
=
1645.17
10000
β100
β16.4517%
(Over 5 years accumulated)
d) How long does it take to earn \$15,000
** Express terms in units of compounding (i.e. from this example, months)**
5 years
\$10,000
\$11,645.17
X 60
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