Summary Economic applications of financial economics

EECM 3714
Lecture 7: Unit 7
Financial Mathematics
Renshaw, Ch. 10, 12, 13

23 March 2022

,OUTLINE
1. Arithmetic and geometric series
2. Compounding
3. Discounting
4. Investment appraisal
5. Bonds and interest rates
6. Loan repayments
7. Annuities

,OBJECTIVES

• Use the geometric series to find the rate at which non-renewable resources are exhausted
• Find the present and future values of payments, deposits, receipts, etc.
• Find the effective interest/growth rate
• Investment appraisal using NPV and IRR
• Find the present and future values of an annuity; find the monthly deposit required for an an
of a specified value
• Find the instalment required to pay back a loan in a specified period of time

, ARITHMETIC SEQUENCE & SERIES

• Sequence = ordered list of elements/numbers
• Arithmetic progression: A sequence in which the next term in the sequence is found by add
constant to the previous term in the sequence, e.g. 1,2,3,4, ...
• The difference between consecutive terms in the sequence is constant
• Consider the sequence 𝐴, 𝐴 + 𝑑, 𝐴 + 2𝑑, 𝐴 + 3𝑑, … − 𝐴 = the initial value/starting value, 𝑑
common difference (note: difference between each term in the sequence is 𝑑)
• Arithmetic series: the sum of the terms of an arithmetic progression
• To get the nth term in the sequence, use 𝐴 + 𝑛 − 1 𝑑
• The sum of the first 𝑛 terms of an arithmetic sequence is
𝑛
• 𝑛 = 𝑆𝑛 and is equal to 2𝐴 + 𝑛 − 1 𝑑
2
• Finance applications: (i) simple interest (interest not reinvested/recapitalised); (ii) invest
paying out a fixed amount every period (e.g. fixed-coupon bond)
• See example 10.2 (322-2)