Annuity Accumulation & Payout Calculations

Annuities involve two distinct phases: the accumulation phase (building value) and the payout phase (receiving income). Understanding how to calculate values and payments in each phase is essential for insurance producers.

What Is an Annuity?

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.

Two Phases of Annuities

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the fund: - Premiums paid: Single lump sum or periodic payments - Tax-deferred growth: Earnings not taxed until withdrawn - Account value grows: Through interest, dividends, or investment gains - No distributions: Owner not receiving income payments yet - Surrender option: Can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

Accumulation Phase Calculations

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

Payout Phase Calculations

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

Exclusion Ratio (Taxation)

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

Surrender Value Calculations

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

Annuity Units (Variable Annuities)

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)

Practical Examples

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

Key Exam Concepts

• 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