The following recurrence relation models the value,
The value of
CORE, FUR2 2021 VCAA 6
Sienna invests $420 000 in a perpetuity from which she will receive a regular monthly payment of $1890.
The perpetuity earns interest at the rate of 5.4% per annum.
- Determine the total amount, in dollars, that Sienna will receive after one year of monthly payments. (1 mark)
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- Write down the value of the perpetuity after Sienna has received one year of monthly payments. (1 mark)
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- Let
be the value of Sienna's perpetuity after months. - Complete the recurrence relation, in terms of
, and , that would model the value of this perpetuity over time. Write your answers in the boxes provided. (1 mark)
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,
CORE, FUR2 2020 VCAA 10
Samuel now invests $500 000 in an annuity from which he receives a regular monthly payment.
The balance of the annuity, in dollars, after
- Calculate the balance of this annuity after two months if
. (1 mark)
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- Calculate the annual compound interest rate percentage for this annuity if
. (1 mark)
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- For what value of
would this investment act as a simple perpetuity? (1 mark)
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CORE, FUR1 2018 VCAA 21 MC
Which one of the following recurrence relations could be used to model the value of a perpetuity investment,