FNCE10001 Finance 1 Lecture 5: Introduction to Financial Mathematics (3)
Carsten Murawski 14 March 2011

Today

What will be the two most important financial decisions during your life?

Learning Objectives

•  Compute the value of a reducible loan •  Value perpetuities

Reducible Loans

•  Borrower makes a series of regular payments, R, for
the term of the loan. Each repayment: –  pays the interest due for that period, and –  repays part of the amount (principal) borrowed

•  Repayments form an ordinary annuity:
A = R*PVAF where A is the principal borrowed, and equals present value of annuity

Reducible Loans

1+ \$100 •  Usually A is known and= (1.055)8 the repayment (R) must be found: = \$65.16 A 1 ￿ R= =￿ r −kt P V AF 1−(1+ k )
r k

PV

=

￿

F

￿ r 8 k

R =

A 1 ￿ ￿ = r −kt P V AF 1−(1+ k )
r k

=

= 1574.70

￿

200000 ￿ 0.072 −12×20 1−( 12 )
0.072 12

R = R × P V AF

Reducible Loans (cont’d)

PV

Example: Say you borrow purchase a house at 7.2% pa compounding monthly, and agree to A 1 make monthly repayments for 20 years. Find the ￿ ￿ R= = r −kt 1−(1+ k ) monthly repayment. P V AF r
k

1+ \$100 = (1.055)8 \$200,000 to = \$65.16

=

￿

F

￿ r 8 k

R =

A 1 ￿ =￿ r −kt P V AF 1−(1+ k )
r k

=

= 1574.70

￿

200000 ￿ 0.072 −12×20 1−(1+ 12 )
0.072 12

R = R × P V AF = 1574.70 ×

12 0.072 © Copyright The University of Melbourne (Department of Finance) 2011 12

1−

= 173035.07

￿ 0.072 ￿−12×15

r k

A 1 ￿ ￿ R = = Reducible Loans (cont’d) r −kt P V AF 1−(1+ k )
r k 0.072 owe? 12 = 1574.70 Present value of the remaining payments:

200000 ￿ lottery. −12×20 ￿ = After 5 years, you win the (1+... [continues]

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