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CA (630,000)

UTSC (30,000)

Mathematics (1,000)

MATA32H3 (200)

Raymond Grinnell (100)

Lecture 5

Department

MathematicsCourse Code

MATA32H3Professor

Raymond GrinnellLecture

5This

**preview**shows half of the first page. to view the full**3 pages of the document.**MATA 32 – Lecture 5 – Annuities and Limits

Annuities:

Annuities are a sequence of payments of a fixed amount made at regular intervals of

time

Ordinary annuity: Paid at end of intervals

Annuity due: Paid at start of intervals

Formulas for the ordinary annuity (i.e. FV and PV) can be modified for annuity due

o payment amount

o interest per payment period

o total number of payments in the compounding sequence

of an ordinary annuity = ∑( of all ordinary payments)

of an ordinary annuity = ∑( of all ordinary payments)

Example:

At the end of each of 4 years, we pay $100 () into an ordinary annuity and interest is 9% APR.

What is the present value (PV) of the annuity?

How to Interpret PV = $323.97:

Year 1:

; Payment #1

; Instant amount after payment #1 is made

PV: amount of money needed to invest

in order to issue future payments

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