Annuity as a Recurrence Relation (HSC SSCE Mathematics Standard): Flashcards

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Annuity as a Recurrence Relation
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Definition of an annuity

Regular, repeated contributions of money over time

What future value represents in an annuity

Total worth of investment at specified end date

Two components of future value

Total contributions + compound interest earned

Definition of recurrence relation

Uses each previous result to generate next value

Recurrence relation formula for investments

Vn+1=Vn(1+r)+DV_{n+1} = V_n(1 + r) + D

Recurrence relation formula for loans

Vn+1=Vn(1+r)DV_{n+1} = V_n(1 + r) - D

What DD represents in annuity formula

Payment per period

What rr represents in annuity formula

Interest rate per period (decimal)

Convert annual rate to monthly rate

Divide by 12

Memory aid: investment vs loan formula difference

Investment uses +D, loan uses -D

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