Definition

An annuity is a contract between an individual and an insurance company that provides:
- Accumulation: Tax-deferred growth of funds
- Distribution: Regular income payments (typically for life)

Opposite of Life Insurance

• Life insurance: Protects against dying too soon
• Annuity: Protects against living too long (outliving savings)

Key Purpose

Liquidate principal systematically while providing guaranteed lifetime income.

Accumulation Phase (Pay-In Period)

Building the fund:
- Premiums paid: Single lump sum or periodic payments
- Tax-deferred growth: Earnings not taxed until withdrawn
- Account value grows: Through interest, dividends, or investment gains
- No distributions: Owner not receiving income payments yet
- Surrender option: Can withdraw value (may have penalties)

Annuitization/Payout Phase (Pay-Out Period)

Receiving income:
- Regular payments: Monthly, quarterly, or annual income
- Principal liquidated: Account value systematically distributed
- Cannot surrender: Usually irreversible once annuitized
- Guaranteed income: Payments continue per contract terms
- Tax on earnings: Portion of each payment taxable

Single Premium Accumulation

Formula: Compound Interest

Future Value = Premium × (1 + Interest Rate)^Years

Example 1: Fixed Interest

Single premium: $100,000
Interest rate: 4% annually
Years: 10

FV = $100,000 × (1.04)^10
FV = $100,000 × 1.480 = $148,024

Gain: $48,024 (tax-deferred)

Example 2: Different Time Periods

Single premium: $50,000
Interest rate: 5% annually

After 5 years: $50,000 × (1.05)^5 = $63,814
After 10 years: $50,000 × (1.05)^10 = $81,444
After 20 years: $50,000 × (1.05)^20 = $132,665
After 30 years: $50,000 × (1.05)^30 = $216,097

Level Premium Accumulation

Formula: Future Value of Annuity Due

FV = Payment × [((1 + r)^n - 1) / r] × (1 + r)

Where:
- Payment = Premium amount
- r = Interest rate per period
- n = Number of periods
- (1 + r) = Beginning of period payment adjustment

Example:

Annual premium: $5,000
Interest rate: 4%
Years: 20

FV = $5,000 × [((1.04)^20 - 1) / 0.04] × 1.04
FV = $5,000 × [(2.191 - 1) / 0.04] × 1.04
FV = $5,000 × [1.191 / 0.04] × 1.04
FV = $5,000 × 29.78 × 1.04
FV = $154,852

Total premiums paid: $5,000 × 20 = $100,000
Interest earned: $154,852 - $100,000 = $54,852

Flexible Premium Accumulation

Variable premiums - calculate year by year:

Example:

Year 1: $10,000 paid, grows at 5%
Year 2: $12,000 paid
Year 3: $8,000 paid
Year 4: $15,000 paid
Year 5: Calculate total value

Year 1 contribution after 5 years:
$10,000 × (1.05)^5 = $12,763

Year 2 contribution after 4 years:
$12,000 × (1.05)^4 = $14,586

Year 3 contribution after 3 years:
$8,000 × (1.05)^3 = $9,261

Year 4 contribution after 2 years:
$15,000 × (1.05)^2 = $16,538

Year 5 contribution (just paid):
$0 (no growth yet)

Total value end of Year 5: $53,148

Factors Affecting Payout Amount

Payment amount determined by:

1. Account value: Amount accumulated or premium paid
2. Annuitant's age: Older = higher payment (shorter life expectancy)
3. Gender: Females live longer = lower payment (where permitted)
4. Interest rate: Higher rates = higher payments
5. Payout option: Type of annuity selected
6. Payment frequency: Monthly, quarterly, annual

Life Annuity Payment Calculation

General concept:

Payment = Account Value / Present Value Factor

Where Present Value Factor based on:
- Life expectancy
- Interest rate (discount rate)
- Payout option

Immediate Annuity Examples

Example 1: Basic Life Annuity

Premium paid: $200,000
Annuitant: Male, age 65
Life expectancy: 20 years
Assumed interest rate: 4%

Using annuity factor table:
Present value factor (life, 20 years, 4%): 13.590

Annual payment = $200,000 / 13.590 = $14,717/year
Monthly payment = $14,717 / 12 = $1,226/month

Payments continue for life, even if lives beyond 20 years

Example 2: Different Ages

Premium: $300,000
Interest: 4%

Age 60 (life expectancy ~25 years):
Annual payment: ~$19,200/year ($1,600/month)

Age 65 (life expectancy ~20 years):
Annual payment: ~$22,000/year ($1,833/month)

Age 70 (life expectancy ~15 years):
Annual payment: ~$27,000/year ($2,250/month)

Older age = higher payment (fewer expected years)

Period Certain Annuity

Fixed number of years, no life contingency:

Formula:

Payment = Premium / [((1 - (1 + r)^-n) / r)]

Example: 10-Year Period Certain

Premium: $100,000
Interest rate: 4%
Period: 10 years

Payment = $100,000 / [((1 - (1.04)^-10) / 0.04)]
Payment = $100,000 / [(1 - 0.6756) / 0.04]
Payment = $100,000 / [0.3244 / 0.04]
Payment = $100,000 / 8.111
Payment = $12,329/year ($1,027/month)

Guaranteed for exactly 10 years, then stops

Life with Period Certain

Combination: Life payments with minimum guarantee

Example:

Premium: $250,000
Age 65, male
Life with 10-year certain

Payment factors in:
- Life expectancy (20 years)
- Minimum guarantee (10 years)
- Adjustment for guarantee reduces payment slightly

Estimated payment: $17,500/year ($1,458/month)

Vs. straight life: $18,500/year

Reduction: ~$1,000/year for 10-year guarantee

What Is Exclusion Ratio?

Percentage of each payment that is tax-free return of principal.

Formula:

Exclusion Ratio = Total Investment / Total Expected Return

Tax-free portion:

Tax-Free Amount = Payment × Exclusion Ratio

Taxable portion:

Taxable Amount = Payment - Tax-Free Amount

Example Calculation

Premium paid (investment): $200,000
Age 65, male, life expectancy: 20 years
Annual payment: $15,000

Total expected return:
$15,000 × 20 years = $300,000

Exclusion ratio:
$200,000 / $300,000 = 0.667 = 66.7%

Each annual payment:
Tax-free: $15,000 × 0.667 = $10,000
Taxable: $15,000 - $10,000 = $5,000

Annually:
- Receive $15,000
- $10,000 is tax-free (return of principal)
- $5,000 is taxable income (earnings)

After 20 years (if lives that long):
- Recovered full $200,000 investment
- All future payments 100% taxable

If Annuitant Dies Early

Same annuity: Dies after 10 years

Received: $15,000 × 10 = $150,000
Investment: $200,000
Unrecovered: $50,000

Estate deduction:
Final tax return can deduct $50,000 loss

During Accumulation Phase

Before annuitization, can surrender for value:

Formula:

Surrender Value = Account Value - Surrender Charge

Example:

Account value: $150,000
Contract year: 5
Surrender charge schedule: 7% of premiums in year 5
Total premiums: $120,000

Surrender charge: $120,000 × 0.07 = $8,400
Surrender value: $150,000 - $8,400 = $141,600

Amount received: $141,600
Taxable gain: $141,600 - $120,000 = $21,600

Surrender Charge Schedule

Typical declining schedule:

Free Withdrawal Provisions

Many contracts allow penalty-free withdrawals:

Typical: 10% per year

Example:

Account value: $200,000
Free withdrawal amount: 10%

Can withdraw penalty-free: $20,000/year
Surrender charge applies to: Amounts over $20,000

Withdraw $30,000:
- First $20,000: No penalty
- Next $10,000: Surrender charge applies

If Year 5 charge is 6% of excess:
Charge: $10,000 × 0.06 = $600
Net received: $30,000 - $600 = $29,400

Accumulation Units

During accumulation:

Accumulation Units = Premium / Accumulation Unit Value

Value fluctuates with market performance

Example:

Premium: $10,000
Accumulation unit value: $25

Units purchased: $10,000 / $25 = 400 units

If unit value increases to $30:
Account value: 400 × $30 = $12,000

If unit value decreases to $22:
Account value: 400 × $22 = $8,800

Annuity Units

At annuitization, convert to annuity units:

First payment calculation:

Annuity Units = Total Accumulation Value / Annuity Unit Value / AIR Factor

Where AIR = Assumed Interest Rate

Subsequent payments:

Payment = Annuity Units × Current Annuity Unit Value

Example:

Accumulation value: $500,000
Annuity unit value: $50
AIR: 4%

Annuity units: 10,000 units
First payment: $5,000

Next month:
If return > 4%: Payment increases
If return < 4%: Payment decreases
If return = 4%: Payment stays same

Month 2 - market up 1%:
Annuity unit value: $51.50
Payment: 10,000 × $51.50 / 12 = $4,292 (monthly)

Example 1: Retirement Planning

Age 45: Start deferred annuity
Annual premium: $10,000
Years to retirement (65): 20 years
Assumed return: 5%

Accumulation at age 65:
FV = $10,000 × [((1.05)^20 - 1) / 0.05] × 1.05
FV = $10,000 × 33.066 × 1.05 = $347,193

Annuitize at 65:
Life annuity, 4% interest assumed
Annual payment: ~$25,500/year ($2,125/month) for life

Total paid in: $200,000
If lives 25 years: Receives $637,500

Example 2: Immediate Annuity Purchase

Age 70, sells business
Takes $800,000 proceeds
Buys immediate annuity

Options compared:

Straight Life:
$5,600/month for life
No survivor benefit

Life with 20-Year Certain:
$5,200/month for life, minimum 20 years
Survivors get payments if dies early

Joint and Survivor (100%):
$4,800/month
Continues to spouse at 100% after death

Period Certain Only (25 years):
$4,200/month for exactly 25 years
No life contingency

• Two phases: Accumulation (pay-in) and Annuitization (payout)
• Accumulation = tax-deferred growth: No taxes until withdrawal
• Older annuitant = higher payment: Shorter life expectancy
• Females = lower payment: Longer life expectancy (where gender rating permitted)
• Higher interest rate = higher payment: Better returns support higher payouts
• Exclusion ratio: Percentage of payment that is tax-free return of principal
• Formula: Exclusion Ratio = Investment / Total Expected Return
• Surrender charges: Declining schedule, typically 7-10 years
• Free withdrawal: Usually 10% per year without penalty
• Annuitization is irreversible: Cannot surrender once annuitized
• Period certain: Pays for specific years, no life contingency
• Life annuity: Pays for life, may outlive expected payments
• Variable annuity units: Accumulation units during growth, annuity units during payout
• AIR (Assumed Interest Rate): Benchmark for variable annuity payments
• Present value factor: Used to calculate payment from lump sum
• Compound interest: FV = Premium × (1 + r)^n