1. Find the maturity value of
a) a $2500 loan for 18 months at 12% simple interest,
b) a $1200 loan for 120 days at 8.5% ordinary simple interest, and
c) a $10 000 loan for 64 days at 15% exact simple interest.
2. At what rate of simple interest will
1
a)
MA170 Week 4 Report: Compound Interest, Fractional Time
Name: _SOLUTIONS_
Lab
Student Number:
Spring 2012
1. [3 marks] Determine the principal that must be invested into a fund to ensure that after 2 years the total value of
the investment reaches $5000 i
MA170 Week 5: Compound Interest - Applications of Compound Interest
Name: _SOLUTIONS_
Lab
Student Number:
Spring 2012
1. [4 marks] Kate Austen borrows $4,000 at a rate of 15% compounded monthly. She is to repay the debt with 4
equal payments. The rst paym
MA170 Week 6 Lab Notes
Unknown Rate and Unknown Time (2.5):
jm
Recall that S = P (1 + i)n represents the accumulated value of an initial investment P at interest rate i =
m
compounded m times per year for t years (n = tm).
1. If S; P; and n are known, the
MA170 Week 13 Lab Notes
Bonds:
A written contract between the issuer (borrower) and the investor (lender) which promises to pay a stated amount (or
amounts) of money at some future date (or dates). Lender is paid interest on investment throughout the term
MA170 Week 13 Report Bonds
Name: _SOLUTIONS_
Lab
Student Number: _
Spring 2012
1. [ 4 marks] Determine whether each of the following bonds are purchased at premium or discount and the
amount of premium or discount, without nding the purchase price. Where
Section 2.5
Determining the Rate
Given S, P, and n, find the unknown interest rate i from
S= P(1+i)
n
(7)
Solving for i , we get :
(1+i)
n
= S/P
and
1/n
1 + i = (S / P )
And thus,
1/n
i =(S/P)
- 1
Since i = jm / m , then jm = m i .
And thus, the nominal a
Section 2.3 : Discounted Value at Compound Interest
The accumulated value of P after n periods at compound
interest rate i is given by
S=P(1+i)" (7)
Given the accumulated value 8, the principal can be found by
solving for Pfrom Formula (7), Le:
S -n
P
kévkm § . \ Compound Interest Formula
Compound Interest: Motivation
0 Simple interest is easy to compute, but its practical applications are limited
0 Recall that the sequence of effective rates of simple interest
,:S(n)S(n1) r
n =, =1,2,3,...
5(n1)
MA170 Week 12 Report: Sinking Funds
Name: _SOLUTIONS_
Lab
Student Number: _
Spring 2012
1. [8 marks] A company has two available sources willing to lend them $250,000 for an 8 year period. The rst
source has offered them the money in the form of an amorti
MA170 Lab Notes - Week 11
Text Reference: 5.1 - 5.3
Amortization of a Debt/Loan (5.1):
Amortization of a loan refers to the repayment of a loan in installments made periodically over some period of time.
If a loan is amortized with equal payments, then th
MA170 Week 3 Lab Notes
Simple Interest (1.1, 1.2)
De nitions:
1. P - Principal (or Present Value or Price).
2. r - Rate of interest.
3. I - Interest earned.
4. t - Length of time money is borrowed/invested.
5. S - Accumulated (or future) value.
Equations:
- The domain of an exponential function consists of all real numbers.
-The graph of an exponential fcn has y-intercept (0,1) and no x-intercept.
1
2
A logarithm of a number is an exponent.
-The exponential fcn and the logarithmic fcn are inverse fcns.
-Th
MA170 Mock Final Exam
Name:
Time Allowed: 120 minutes
Total Value: 100 marks
Number of Pages: 9
Instructions:
Cheat Sheet:
One 8:5" 11" page of study notes (both sides) is allowed as a reference
while completing the mock test. Please note, that the cheat
Equations of Value
Time Value of Money
0 A sum of money available right now is worth more the promise of the same
amount at some definite time in the future
o If interest can be earned, a sum of money grows to a larger amount if invested
- If a financ
MA170 Week 6: Progressions, Ordinary Annuities
Name: _SOLUTIONS_
Lab
Student Number: _
Spring 2012
1. [3 marks] Rich Uncle Moneybags makes the following offer to his nephew:
(i) $2,000,000 immediately
(ii) $0.01 (a penny) today, $0.03 tomorrow, $0.09 on t
MA170 Week 4 Lab Notes
Simple Interest (1.1, 1.2): See Week 2 and Week 3 Lab Notes
Equations of Interest:
I = P rt
S = P + I = P + P rt = P (1 + rt)
P = S(1 + rt)
1
Equations of Value (1.3): See Week 3 Lab Notes
Partial Payments (1.4):
Financial obligatio
MA170 Week 8: Applications of Annuities, Determining the Term and Rate
Name: _SOLUTIONS_
Lab
Student Number: _
Spring 2012
1. [7 marks] Every 10 years a manufacturing rm must replace some of its machinery. The cost of an individual
machine is $38 400. To
MA170 Week 3 Report: Equations of Value at Simple Interest; Partial
Payments; Simple Discount
Name: _SOLUTIONS_
Lab
Student Number:
Spring 2012
1. [ 5 marks ] A loan of $1,500 with a simple interest rate of 9% is due in 11 months. The borrower makes parti
MA170 Lab Notes - Week 3
Compound Interest (2.1, 2.3):
De nitions:
1. P - Principal/Initial investment or present/discounted value of S:
2. S - The future/accumulated value of P .
3. n - Total number of compounding periods in term of the investment.
4. m
MA170 Week 2 Report: Applications of Accumulated & Discounted Value at
Simple Interest; Equations of Value
Name: _SOLUTIONS_
Lab
Student Number:
Spring 2012
Show your work. Marks may be deducted for incomplete solutions. Unless otherwise stated, use exact
MA170 Week 2 Lab Notes
Simple Interest (1.1)
De nitions:
1. Principal P - Initial amount of money (capital) invested or borrowed.
2. Rate of interest r - annual percentage earned on the original investment of P .
3. Amount of simple interest earned I - gi
MA170 Week 8 Lab Notes
Other Simple Annuities (3.4):
1. Annuity Due:
An annuity whose periodic payments are made at the beginning of each payment/interest period (instead of the
end as in an ordinary annuity).
Notes:
! Accumulated value S of an annuity du
Lecture 8: Other Applications of Compound Interest.
Continuous Compounding
MA170: Introduction to Mathematics of Finance
June 2, 2014
Mathematics of Finance (MA170)
Lecture 8: Other Applications of Compound Interest. Continuous Compounding
June 2, 2014
1/
Lecture 1: Introduction
MA170: Introduction to Mathematics of Finance
May 5, 2014
Mathematics of Finance (MA170)
Lecture 1: Introduction
May 5, 2014
1/1
Outline
Mathematics of Finance (MA170)
Lecture 1: Introduction
May 5, 2014
2/1
Interest Theory
Topics
Lecture 2: Simple Interest and Discounted Value
MA170: Introduction to Mathematics of Finance
May 7, 2014
Mathematics of Finance (MA170)
Lecture 2: Simple Interest and Discounted Value
May 7, 2014
1 / 19
Outline
1 Simple Interest (Continued from Lecture 1
]
MAl 70 Notes 1
1.1 - Simple Interest
Interest - A fee that a borrower pays to a lender for the use of the lender's money.
Some motivation for interest:
1. Would you rather have $100 today or $100 next week?
2. Inflation - things usually cost more in th