Annuity Basics and Pricing Concepts

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Questions and Answers

What is the monthly unindexed income stream from a lump sum of $100,000 based on the given calculations?

$800

$900

$717.67 (correct)

$600

How much would a 25-year annuity with a required income stream of $2,000 per month cost if indexed at 3%?

$380,000

$413,000 (correct)

$350,000

$500,000

What is the formula to calculate the indexed term certain annuity based on the content provided?

an:i:g(p) = 100,000 / 14.71708 (correct)

an:i:g(p) = a(p)n:i:g × i

an:i:g(p) = initial amount / annuity factor

an:i:g(p) = i(i(p))

If the indexed income stream in the first year is $566.24, what would it be in the second year assuming a 3% increase?

$583.22 Signup and view all the answers

Which of the following correctly describes the effect of a higher interest rate on the cost of an annuity?

It decreases the total cost. Signup and view all the answers

What is the relationship between the amount spent on an annuity and the annuity payment?

Higher amounts lead to higher annuity payments. Signup and view all the answers

Which element is essential for determining the Retirement Income Stream (RIS) from a lump sum?

The interest rate level Signup and view all the answers

What type of annuities does the content focus on for pricing?

Term certain annuities Signup and view all the answers

Which feature characterizes an ordinary annuity?

Payments occur at the end of regular intervals. Signup and view all the answers

What might near retirees prefer regarding their lump sum investments?

Avoid equities and seek stable income sources. Signup and view all the answers

In the pricing formula for an ordinary annuity, what does the variable R represent?

The periodic payment amount Signup and view all the answers

How does the interest yield impact the RIS from a lump sum?

Higher interest yields lead to greater RIS. Signup and view all the answers

What is the implication of choosing a longer term for an annuity?

Each annuity payment becomes lower. Signup and view all the answers

What is the present value required to pay for each dollar of an annuity given a yield of 5.5% over 15 years?

$10.0375809 Signup and view all the answers

Which of the following corresponds to the annual amount received from a $300,000 investment at the present value factor of $10.0375809?

$29,887.68 Signup and view all the answers

What is a characteristic of term certain annuities compared to annual annuities?

They typically have more frequent payment intervals. Signup and view all the answers

Which of the following factors is not applicable for complying annuities post-2007?

New purchases allowed Signup and view all the answers

What is the effect of having a residual capital value (RCV) at the end of a term certain annuity?

It reduces the amount of the annuity stream purchased. Signup and view all the answers

If an annuity of $100,000 is indexed at a rate of 3% in the second year, what adjustment is made to the payment at the beginning of the second year?

$A(1.03/12) Signup and view all the answers

Given the parameters of a unindexed term certain annuity with a yield of 6.19%, what is the calculated monthly interest rate using the formula: i(p) = p[(1+i)^(1/p)-1]?

0.0602103 Signup and view all the answers

In the context of annuities, what does the term 'unindexed' signify?

Payments remain fixed throughout the term. Signup and view all the answers

Study Notes

Annuity Basics:

Annuity: A financial product that provides a stream of regular payments for a defined period.
Lump Sum: A one-time payment made to purchase an annuity.
Factors Affecting Annuity Payments:
Lump Sum: Larger lump sums result in higher annuity payments.
Annuity Term: Longer terms result in lower individual payments.
Interest Rate: Higher interest rates result in greater returns for the annuity holder.

Near Retirees and Annuities:

Near Retirees: Face the decision of maximizing their retirement income stream (RIS).
Risk Aversion: Many near retirees are averse to equity market risk, often choosing annuities over direct investments.
Age Pension: Can supplement RIS for retirees with lower lump sum accumulations.

Pricing of Annuities and Pensions:

Ordinary Annuity: Used to price annuities and pensions, with payments made at the end of regular intervals.
Pricing Formula: Key variables include:
Interest Rate (i): The effective rate of interest per payment interval.
Term (n): Fixed number of payment intervals.

Annuity Example:

Example: A retiree wanting to spend $300,000 on a 15-year annuity at 5.5% p.a., needs to pay $10.0375809 for each annual dollar of annuity.
Annual Payment: The annual amount received would be $29,887.68.

Term Certain Annuities and Pensions:

More Practical: Monthly payments over a fixed term are more common than annual payments.
Fixed Interest Rate: The interest rate is fixed for the term.
Indexation: Payments can be indexed to inflation or other factors.
Restrictions on "Complying" Annuities: Exist for certain pre-2007 annuities.

Cost of Term Certain Annuities:

Unindexed vs. Indexed: Unindexed annuities have fixed payments, while indexed annuities adjust for inflation.
Example: A 20-year monthly annuity at 6.19% costing $100,000:
Unindexed: Upfront cost of $11.61206 per dollar of annuity, resulting in total annual income of $8,612.
Indexed (3.0% p.a.): Upfront cost of $14.70708 per dollar of annuity, with monthly payments increasing over time.

Term Certain Annuity Calculations:

Unindexed: The up-front cost is calculated using a formula that accounts for the periodic interest rate i(p), derived from the annual interest rate (i) and payment frequency (p).
Indexed: The formula includes an indexation term (g) that reflects the annual growth rate.

Term Certain Annuity Example:

Case: A 65-year-old requiring a 25-year annuity with a monthly RIS of $2,000, indexed at 3%.
Cost: The up-front cost would be approximately $413,000.
Interest Rates: A higher interest rate would lead to a lower up-front cost.

Key Takeaways:

Annuities provide a guaranteed stream of income for a defined period.
Choosing the right annuity depends on individual circumstances and financial goals.
Key considerations include the lump sum available, the desired term, and the interest rate offered.
Understanding the different types and pricing of annuities is essential for making informed decisions.

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Description

This quiz covers fundamental concepts related to annuities, including their definitions, the factors affecting payment amounts, and the differences between lump sums and annuities. It also addresses the considerations near retirees face when choosing annuities and the pricing formulas used for ordinary annuities and pensions.