Chapter 2. Equations of Value and Yield Rates
ACTSC231 — Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Fall 2010
Instructor: Chengguo Weng
C. Weng ([email protected])
– p. 1/1

Simple Eq. of Value
•
Eq. of value with a single payment:
A
K
(
T
) =
K
(1 +
i
)
T
XBox
K
——investment amount/capital/contribution made at time 0
XBox
A
K
(
T
)
——accumulated value at time
T
XBox
T——length of investment period
XBox
(annual) effective interest rate
•
Example 2.1:
Anita’s aunt opens an account and deposits
$
C
for her. The
account earns compound interest with an annual effective interest rate of 8%.
Five years after the account was open, Anita closes the account and received
$3,673.32. Find
C
.
C. Weng ([email protected])
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Simple Eq. of Value
•Example 2.2:Anita deposits$400in an account that grows by compoundinterest. After 5 years the balance has grown to$463.71. What’s the annualeffective interest rate this account earns?

Simple Eq. of Value
•
Example 2.3:
John borrows $1,000. The loan is governed by compound interest
at an annual effective interest rate of 10%. John repays $600 at the end of the
one year and plan to complete repayment of the loan with a payment of
$
P
at
the end of the second year. Find
P
.
Consider time 0, time 1 and time 2 equations of value respectively.
C. Weng ([email protected])
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