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Questions and Answers
What is the monthly unindexed income stream calculated from $100,000?
What is the monthly unindexed income stream calculated from $100,000?
- $900.00
- $717.67 (correct)
- $800.50
- $832.00
What is the cost required for a 25-year annuity that pays $2,000 per month at a 3% indexation?
What is the cost required for a 25-year annuity that pays $2,000 per month at a 3% indexation?
- $500,000
- $345,000
- $413,000 (correct)
- $400,000
How much would the monthly amount increase in the second year of an indexed annuity, starting from $566.24?
How much would the monthly amount increase in the second year of an indexed annuity, starting from $566.24?
- $583.22 (correct)
- $550.12
- $600.00
- $570.00
What determines the increase in payment for an indexed annuity after the first year?
What determines the increase in payment for an indexed annuity after the first year?
Which of the following statements about the cost of annuities is correct?
Which of the following statements about the cost of annuities is correct?
What is the characteristic of the periodic payments in an ordinary annuity?
What is the characteristic of the periodic payments in an ordinary annuity?
How is the cost of an annuity generally determined?
How is the cost of an annuity generally determined?
What term means an annuity that pays a fixed amount over a specified time period?
What term means an annuity that pays a fixed amount over a specified time period?
In the annuity example given, what total annual payment would result from a $300,000 investment at a 5.5% yield?
In the annuity example given, what total annual payment would result from a $300,000 investment at a 5.5% yield?
What is the present value calculation used to find the amount R in the ordinary annuity formula?
What is the present value calculation used to find the amount R in the ordinary annuity formula?
What is the implication of taking a lump sum from an accumulation at retirement?
What is the implication of taking a lump sum from an accumulation at retirement?
What aspect does pricing for pensions and term certain annuities consider in its calculations?
What aspect does pricing for pensions and term certain annuities consider in its calculations?
Which of these statements about indexed annuities is true?
Which of these statements about indexed annuities is true?
What is the formula for calculating the monthly interest rate when payments are made monthly?
What is the formula for calculating the monthly interest rate when payments are made monthly?
Which factor can affect the cost of an indexed annuity compared to an unindexed annuity?
Which factor can affect the cost of an indexed annuity compared to an unindexed annuity?
What is a unique characteristic of term certain annuities mentioned in the content?
What is a unique characteristic of term certain annuities mentioned in the content?
What is the cost of a 20-year unindexed annuity if the upfront cost per annual dollar is $11.61206?
What is the cost of a 20-year unindexed annuity if the upfront cost per annual dollar is $11.61206?
In the first year of an indexed annuity, how is the payment amount adjusted for the second year?
In the first year of an indexed annuity, how is the payment amount adjusted for the second year?
What distinguishes a complying annuity from a non-complying annuity?
What distinguishes a complying annuity from a non-complying annuity?
How is the term 'unindexed' defined regarding term certain annuities?
How is the term 'unindexed' defined regarding term certain annuities?
If an annuity is indexed at 3.0% p.a., how does this affect the payments after the first year?
If an annuity is indexed at 3.0% p.a., how does this affect the payments after the first year?
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Study Notes
Term Certain Annuities and Pensions
- Term certain annuities are paid at regular intervals (monthly, quarterly, annually)
- They are commonly used for pensions
- Typically have a fixed interest rate and a fixed term
- These annuities can be indexed to inflation
Cost of Term Certain Annuities
- The cost of a term certain annuity depends on the period of the annuity, the interest rate, and whether it is indexed.
- The formula used to calculate the cost of an unindexed annuity is a(p)n:i
- The formula used to calculate the cost of an indexed annuity is a(p)n:i:g
- For a $100,000 unindexed term certain annuity with a 6.19% yield, the cost would be $11.61206 per dollar of annuity
- For a $100,000 indexed term certain annuity with a 6.19% yield and 3% p.a. indexation, the cost would be $14.70708 per dollar of annuity
Pricing of Annuities (and Pensions)
- Annuities are priced as ordinary annuities, meaning payments are made at the end of each period.
- The formula used to calculate the PV of an annuity is An = R[1- (1+r)-n]/r
- This formula can be used to determine the amount to draw down under an account-based pension.
Annuity Example
- A retiree wanting a $300,000 annuity for 15 years at 5.5% p.a. yield would have to pay $10.0375809 for each annual dollar
- The annual amount received for this annuity would be $29,887.68
- For a monthly payment unindexed annuity, the monthly amount would be $717.67
Indexed Term Certain Annuity
- An indexation rate (g) is applied at the start of each year after the first year, to reflect inflation
- The formula used to calculate an indexed annuity is a(p)n:i:g
- For the indexed annuity from previous example, the monthly indexed income stream in the first year would be $566.24 per month
- This monthly amount would increase each year due to the indexation.
Term Certain Annuities: Example Application
- For a 65-year-old wanting a 25-year annuity with a $2,000 monthly return indexed at 3% p.a.
- This would cost ~$413,000
- The cost of a term certain annuity is dependent on the interest rate, a higher interest rate lowers the cost.
- For example, if the interest rate was 8% p.a., this annuity would cost ~$345,000.
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