Formula Sheet
S (u + 1) S (u )
S (u )
Compound interest
(1 + i )t
Simple interest
(1 + ti )
vt = (1 + i ) t
(1 + it ) 1
Effective rate of interest: iu +1 =
Payment of 1
Accumulated value after
t years
Present value at time 0
i paid at the end of the perio
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 7
Where possible, you should perform the calculations exactly, however in some cases you
will need to use linear interpolation.
Question 1
A bank lends a company $5,000 at a fixed rate
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Week 12
Stochastic Interest Rate Models
Deterministic approach - 'i' is known and fixed in advance.
However, in practice, future interest rates are uncertain. We can
model the uncertainty in future intere
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Week 10
Arbitrage
Describes a risk free trading profit
An arbitrage opportunity exists if either:
a. an investor can make a deal that would give her or him an
immediate profit, with no risk of future loss
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Lecture Week 6
Loans
Example: A bank lends an individual $1,000 for three years in
return for three payments of X at the end of each year. The bank
charges an effective rate of 7% pa. Find X.
Loan Repayme
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Lecture Week 5
Equations of value
Financial transactions involve cash inflows and cash outflows.
Equations of value set the value of all cash inflows equal to the
value of all cash outflows at a common ti
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Lecture Week 7
Measuring investment performance
What factors drive the fund value to increase/decrease?
Two ways we can measure this investment performance
1. Money Weighted Rate of Return
2. Time Weighte
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Week 9
Effect of term to redemption on the yield
When P C, the yield j depends on the term to maturity n.
Why?
Because n determines the timing of the capital gain/loss. It is
preferable to receive a capit
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Week 13 - Revision
Question 1
The table below gives information about an investment fund (all
figures in $m):
2011
2012
2013
Value of fund at 1 January
620
Value of fund at 30 April
700
710
850
Net cashfl
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Lecture Week 8
Fixed interest securities
Governments/corporations may raise money by issuing fixed
interest securities (also known as bonds) to investors
Some questions we are going to answer:
Given the
STAT 2032/6046:
Financial Mathematics
Abhinav Mehta
Week 2
Question
What deposit made today will provide for a payment of $1000 in
1 year and $2000 in 3 years, if the effective compound rate of
interest is 7.5% pa?
The present value of the 2 payments is:
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 2
Question 1
$2,500 is invested. Find the accumulated value of the investment 10 years after it is made
for each of the following rates.
(a) 4% annual simple interest
(b) 4% effective a
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 6
Question 1
The present value of two payments of $100 each to be made at the end of n years and 2n
years is $100. If i=0.08, find n.
Question 2
This question mentions shares and divide
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 3
Question 1
Find the present value of $1000 due at the end of 10 years if
(a) i (2) = 0.09 , (b) i (6) = 0.09 , and (c) i (12) = 0.09 .
Question 2
Mountain Bank pays interest at a nomi
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 4
Question 1
12 payments of $2,000 each are made at 2-year intervals. Find the value of the series
(a) 2 years before the first payment at annual effective interest rate i = 0.08 ,
(b)
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 5
Question 1
Calculate values for the following functions:
a) a7 at interest rate of 7.5% per annum effective.
b) Ia 5 at interest rate of 10% per annum effective.
c) 15 at a nominal ra
SCHOOL OF FINANCE AND APPLIED STATISTICS
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 8
Question 1
This question refers to two projects relating to a small software company that has asked
to set up a new computer system for a majo
SCHOOL OF FINANCE AND APPLIED STATISTICS
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL EXERCISES WEEK 9
Question 1
A 25 year bond has a face value of $10,000 and is redeemable at $12,000. The bond pays
coupons of 8.0% half-yearly. Find the price
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Week 11
Interest rate risk
The value of a fixed interest portfolio will fluctuate as interest
rates vary. As a portfolio manager, you need to manage changes
in the portfolio value due to changes in intere