8.2 Annuities
3 min read•june 18, 2024
Annuities are a key financial tool, offering a series of equal payments over time. They come in two main types: ordinary annuities with end-of-period payments, and annuities due with start-of-period payments. Understanding these can help you make smarter financial decisions.
Calculating the of annuities is crucial for financial planning. The formulas for ordinary annuities and annuities due help determine the current worth of future payment streams. This knowledge is vital for various applications, from lottery payouts to retirement planning and .
Annuities
Definition of annuity types
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- refers to a series of equal payments made at fixed intervals over a specified period (monthly, quarterly, annually)
- Payments can be made at the beginning () or end () of each period
- makes payments at the end of each period (rent payments, car payments, bond interest payments)
- makes payments at the beginning of each period (lease payments, insurance premiums)
Present value of annuities
- (PVOA) calculates the current value of a series of future payments made at the end of each period
- Formula:
- represents the periodic payment amount
- represents the periodic interest rate
- represents the total number of periods
- Formula:
- (PVAD) calculates the current value of a series of future payments made at the beginning of each period
- Formula:
- PVAD is higher than PVOA because payments start earlier, allowing for additional compounding
Applications of annuities
- Lotteries offer winners the choice to receive their prize as a or an providing regular payments over a specified period (20-30 years)
- Structured settlements compensate an injured party through a series of payments, usually made through an annuity to ensure long-term financial security (personal injury cases, wrongful death suits)
- Retirement planning uses annuities to provide a steady income stream during retirement years
- Immediate annuities begin payments shortly after purchase (within 12 months)
- Deferred annuities delay payments to a later date, allowing the invested funds to grow tax-deferred (5-10 years or more)
Types of Annuities
- : Provides a guaranteed payout amount for a specified period
- : Offers payouts that can fluctuate based on the performance of underlying investments
- : Increases payouts over time to help maintain purchasing power
- : A unique feature of annuities that can potentially increase returns for those who live longer
Annuities in financial problem-solving
- Calculate the present value of a series of future cash flows to determine the value of a pension plan or a stream of rental income
- Determine the periodic payment amount needed to achieve a specific , such as calculating the monthly savings required to reach a retirement goal
- Use annuity formulas to solve for missing variables in financial scenarios:
- Present value (PV)
- (FV)
- Periodic payment (PMT)
- Interest rate (r)
- Number of periods (n)
- Compare the results of ordinary annuities and annuities due to understand the impact of payment timing on present and future values
Pros and cons of annuities
- Advantages include:
- Guaranteed income stream over a specified period provides financial security
- for deferred annuities allows funds to compound without annual taxation
- Potential for higher returns compared to low-risk investments (CDs, bonds)
- Disadvantages include:
- Lack of as funds are locked in for a set period, limiting access to money
- Potential for lower returns compared to higher-risk investments (stocks, real estate)
- Fees and commissions can reduce overall returns, especially with variable annuities
- Inflation risk means fixed payments may lose purchasing power over time
- Surrender charges may apply for early withdrawal, potentially reducing the value of the investment
Key Terms to Review (32)
Amortization: Amortization is the process of gradually writing off the initial cost of an asset over a set period. It is often used in accounting to allocate the cost of intangible assets such as patents or goodwill.
Amortization: Amortization is the process of gradually reducing a debt or expense over a period of time through regular payments or allocations. It is a key concept in finance that is relevant to various financial statements and time value of money calculations.
Annuity: An annuity is a series of equal payments made at regular intervals over a specified period. These payments can be either incoming (received) or outgoing (paid).
Annuity: An annuity is a series of equal payments made at regular intervals, such as monthly, quarterly, or annually, over a specified period of time. It is a financial instrument that provides a stream of income or payments, and it is commonly used in retirement planning, insurance, and investment strategies.
Annuity due: An annuity due is a series of equal payments made at the beginning of each period. This contrasts with an ordinary annuity, where payments are made at the end of each period.
Annuity Due: An annuity due is a series of equal payments made at the beginning of each period, rather than at the end of the period as in a regular annuity. This type of annuity is commonly used in financial planning and investment analysis to model situations where payments are made upfront, such as rent, insurance premiums, or mortgage payments.
Cash flow: Cash flow is the net amount of cash being transferred into and out of a business. It represents the company's operating, investing, and financing activities over a specific period.
Cash Flow: Cash flow refers to the net amount of cash and cash-equivalents moving in and out of a business or an individual's possession over a given period of time. It is a crucial measure of financial health and performance, as it reflects the ability to generate and manage the inflow and outflow of cash necessary for operations, investments, and financing activities.
Compound Interest: Compound interest is the interest earned on interest, where the interest accumulated on the principal balance of an investment or loan is added to the principal, and the resulting sum then earns additional interest. This process of earning interest on interest creates exponential growth over time, making compound interest a powerful concept in finance.
Constant perpetuity: A constant perpetuity is a financial instrument that pays a fixed amount of money at regular intervals indefinitely. It is valued by discounting the perpetual series of cash flows back to their present value.
Deferred Annuity: A deferred annuity is a type of annuity contract where the annuitant defers the start of annuity payments to a future date, allowing the invested funds to grow tax-deferred until the specified retirement age or income need arises.
Fixed Annuity: A fixed annuity is a type of annuity contract that provides the annuitant with a guaranteed stream of fixed payments, typically for a specified period of time or for the lifetime of the annuitant. It offers a predictable and stable income stream, making it a popular choice for retirement planning and income generation.
Future value: Future value is the amount of money an investment will grow to over a period of time at a given interest rate. It reflects the value of a current asset at a future date based on expected growth.
Future Value: Future value (FV) is the value of an asset or cash flow at a future date, based on a given rate of growth or interest rate. It represents the amount a sum of money will grow to over a certain period of time when compounded at a specific interest rate.
Immediate Annuity: An immediate annuity is a type of annuity contract where the annuitant begins receiving periodic payments immediately after the initial lump-sum premium payment is made. This is in contrast to a deferred annuity, where payments are delayed until a future date. Immediate annuities provide a reliable stream of income for retirees or those seeking to generate a steady cash flow.
Inflation-Adjusted Annuity: An inflation-adjusted annuity is a type of annuity contract that provides periodic payments that increase over time to keep pace with inflation, ensuring the purchasing power of the payouts remains constant. This feature is particularly important in the context of annuities, which are financial instruments designed to provide a steady stream of income during retirement.
Liquidity: Liquidity refers to the ease and speed with which an asset can be converted into cash without significant loss in value. It is a crucial concept in finance that encompasses the ability of individuals, businesses, and markets to readily access and transact with available funds or assets.
Lump sum: A lump sum is a single payment of money, as opposed to multiple payments over time. It is often used in financial contexts where the time value of money is considered.
Mortality Credits: Mortality credits refer to the additional benefits that annuity holders receive as a result of the pooling of longevity risk in an annuity contract. When an annuitant dies, their remaining account balance is distributed among the surviving annuitants, providing them with higher payouts, known as mortality credits.
Ordinary annuity: An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. Examples include mortgage payments, car loan payments, and retirement savings contributions.
Ordinary Annuity: An ordinary annuity is a series of equal payments made at the end of each period over a fixed number of periods. It is a common financial concept that is closely tied to the topics of annuities and equal payments using financial calculators and spreadsheets.
Perpetuity: A perpetuity is an infinite stream of equal cash flows that continues forever. It is a financial concept that describes a situation where a series of payments or cash flows goes on indefinitely without end.
Present Value: Present value is a fundamental concept in finance that refers to the current worth of a future sum of money or stream of cash flows, discounted at an appropriate rate of interest. It is a crucial tool for evaluating the time value of money and making informed financial decisions across various topics in finance.
Present Value of an Annuity Due: The present value of an annuity due is the current worth of a series of equal future payments that begin immediately and continue for a specified period of time. It represents the lump-sum amount that, if invested today at a given interest rate, would be sufficient to make all the future payments of the annuity.
Present Value of an Ordinary Annuity: The present value of an ordinary annuity is the lump-sum amount that, if invested today at a given interest rate, would be equal to the total of all the future periodic payments of the annuity. It represents the current worth of a series of future cash flows from an annuity.
Structured Settlement: A structured settlement is a financial arrangement in which a claimant agrees to resolve a personal injury lawsuit or workers' compensation claim by receiving periodic payments instead of a lump-sum payment. These payments are typically funded by an annuity and are designed to provide the claimant with a steady stream of income over an extended period of time.
Structured settlements: Structured settlements are financial arrangements in which a claimant receives periodic payments instead of a lump sum, often resulting from legal settlements. These payments are typically designed to provide long-term financial security.
Surrender Charge: A surrender charge is a fee imposed by an insurance company when an annuity contract is terminated or surrendered before the end of the contract's term. This charge is designed to recoup the costs associated with issuing and maintaining the annuity contract, and to discourage early withdrawal of funds.
Tax-Deferred Growth: Tax-deferred growth refers to the ability to accumulate investment earnings, such as interest, dividends, or capital gains, without paying income taxes on those earnings until the money is withdrawn, typically during retirement. This feature allows investments to grow at a faster rate compared to taxable accounts, as the reinvested earnings are not reduced by annual tax payments.
Time Value of Money: The time value of money is a fundamental concept in finance that recognizes the difference in value between a sum of money available today and the same sum available at a future point in time. It is based on the principle that money available at the present time is worth more than the identical sum in the future due to its potential to earn interest or be invested to generate a return.
Time value of money (TVM): Time Value of Money (TVM) is the concept that money available now is worth more than the same amount in the future due to its potential earning capacity. This principle underlines why receiving money today is preferable to receiving it later.
Variable Annuity: A variable annuity is a type of annuity contract that allows the contract owner to invest their payments in a variety of investment options, such as stocks, bonds, and mutual funds. The value of the annuity will fluctuate based on the performance of the underlying investments, providing the potential for growth but also carrying investment risk.