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MATH FOR SENIORS

Jerry Tuttle, FCAS, CPCU, MA, MA, MS

Math & Data Analysis adjunct at SNHU

2026

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2026

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AS WE GET OLDER, 4 QUESTIONS

Am I still attractive?
What will my health be?
Will I have enough money?
How long will I live?

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2026

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ME TO CHATGPT: “DRAW A MODERATELY ATTRACTIVE

70-YEAR OLD WOMAN”

How do I know she is attractive?

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2026

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I MEASURE HER, OF COURSE

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2026

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GOLDEN RATIO PHI φ ≈ 1.618

IS METRIC OF BEAUTY

6 phi ratios correlate to facial attractiveness:

Not close. But beauty is in the φ of the beholder.

Six φ Measurements
Face length / width	1.33
Mouth width / interocular	1.33
Mouth width / nose width	1.45
Lips to chin / interocular	1.17
Lips to chin / nose width	1.27
Ear length /nose width	1.27
Average	1.30

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2026

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THE DEMENTIA TEST

The nurse asked me to draw a clock face and to set hands at “ten minutes after eleven”.

I pondered this for awhile.

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2026

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DOES ANYBODY REALLY KNOW WHAT TIME IT IS? DOES ANYBODY REALLY CARE?

Only I would worry about angle θ.

The smaller hand is not on the 11, but 1/6 of the way towards 12. ∴ θ = (5/6)*30 + 60 = 85

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2026

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CREDIT CARD INTEREST

Is your credit card debt growing?
Suppose your interest rate is 24%.
How long will it take for debt to double?

(This is a valid credit card #. Luhn’s algorithm verifies this.)

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2026

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THE RULE OF 72

Rule of 72 says for a fixed annual interest rate I, money that is compounded doubles in approx. N = 72 / I years.
Why does this work?
(1 + I/100)^N = 2, solve for N in terms of I.
Can’t be done! Well, not exactly.
Need to make an assumption that for small x, LN(1 + x/100) approx equals x.
We frequently assume linearity, for example in extrapolating cooking times.
Taylor Series, Newton-Raphson
It’s a linear world – approximately.

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2026

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2 CAVEATS

I am not qualified to give financial advice.
Although I am an actuary, my actuarial code of ethics requires I disclose the following:

I am a casualty actuary, and I am not truly qualified in life expectancy and Social Security. I am providing some math, but not advice.

Does your code of ethics require disclosures when you are less than fully qualified?

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2026

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HOW LONG WILL I LIVE (MEAN) ?

Life expectancies, per Social Security

Age	Male	Female
62	19.61	22.5
70	14.09	16.27
75	10.92	12.68
85	5.75	6.76

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2026

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WHAT IS A LIFE EXPECTANCY?

Life expectancy is the expected value (mean; average) of the remaining lifetime.
It is the sum of:

probability of living 1 yr, +

probability of living 2 yrs, etc.

A life expectancy of 20 years does NOT imply everyone lives 20 years, and then immediately dies! But some calcs do this.
Some of us will live a LOT longer.

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2026

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YOUR SOCIAL SECURITY BENEFIT

Primary Ins Amt (PIA) based on top 35 yrs, if you start at Full Retirement Age, now 67.
30% reduction if start at age 62, eg 100 →70.
24% incr if wait until age 70, eg 100 →124.
Big decision: start at age 62, or wait until 70.

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2026

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BREAKEVEN SOC SEC CALCS

AARP, SmartAsset, others calc total cumulative $ starting at 62 vs starting at 70.
Breakeven is about at age 80.
This is too simplistic because it ignores:
1. Future COLA (cost of living adjustments)
2. Probability of surviving to ea future age
3. Magnitude of $ at higher ages
4. Time value of money
Better analysis uses Mortality-Weighted Expected Value.
For simplicity I will ignore time value of money and married couple survivor benefit.

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2026

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HOW LONG WILL I LIVE (DISTR) ?

25% prob male 62 yr lives to 89

25% prob female 62 yr lives to 92

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2026

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ANNUAL BENEFITS OVER TIME

Benefit @ 89, if started at 62: 37,319

Benefit @ 89, if started at 70: 52,186

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2026

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MORTALITY-WTD EXPECTED VALUE

EV_x = P(alive at age x) * ($ at age x).

Reflects longevity risk, and reflects the likelihood of being alive to collect the $. A more mathematical measure of 62 vs 70.

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2026

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WHAT IF I THINK I WON’T LIVE SO LONG? ADJUSTMENT FOR MODERATE TO SEVERE IMPAIRMENT

25% prob male 62 yr lives to 82

25% prob female 62 yr lives to 85 q _adj = 2* q_x

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HOW LONG WILL I LIVE?

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2026

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MY 10 YEARS OF IGNITE

2016 Stop making excuses for Aunt Sally

2017 Cartoons in Math class

2018 Why do we make you take Math?

2019 Math of love

2020 English & Math teachers

2021 Data science aboard Titanic

2022 (skipped)

2023 Math on the Simpsons

2024 Black hole in number line

2025 Math of Taylor Swift

2026 Math for seniors