Sequence formula needed - Keyword --> annuity

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Discussion Overview

The discussion revolves around finding a formula related to an insurance policy that incorporates an annuity ratio of 6%. Participants explore the implications of this ratio on the returns over time, the nature of the policy, and how to derive a suitable equation for various parameters such as interest rates and coverage years.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a formula to understand the effects of different annuity ratios and maximum return values, indicating boundary conditions such as tenure and known maximum return.
  • Another participant suggests plotting values to visualize the relationship and recommends using an interactive linear regression tool for formula derivation.
  • A different viewpoint raises the importance of considering life tables and the nature of the insurance policy, questioning the adequacy of the payout for income replacement.
  • Some participants identify the amounts in a specific column as a geometric sequence with a ratio of 1.06, referencing a formula for partial sums of geometric sequences.
  • One participant expresses difficulty in deriving the exact sequence despite using suggested resources, noting that a parabola regression was close but not exact.
  • There is a mention of the policy potentially self-financing a level premium at a 6% interest rate, but participants seek a general formula that allows for variable inputs.
  • A participant proposes a death benefit formula but acknowledges that specific numbers should not be fixed in the equation, emphasizing the need for a more adaptable formula.
  • Another participant notes that mortality charges must be considered to derive necessary values, suggesting reliance on the insurance company's mortality table.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact formula needed, and multiple competing views regarding the nature of the policy and the appropriate mathematical approach remain present throughout the discussion.

Contextual Notes

Limitations include the dependence on specific definitions of terms like "annuity ratio" and "mortality charge," as well as unresolved mathematical steps in deriving a general formula for the insurance policy.

k.udhay
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TL;DR
Find out the equation of sequencing numbers; Annuity calculation
Below is a screenshot of an insurance policy:
1723811947308.png


I was told by the insurance company that the return becomes lower and lower with the age till death increasing. And this reduction in return is by an annuity ratio of 6%.

I wanted to find out the formula so that I can understand the effect of different annuity ratio, higher max. return value, compare with other policies etc. But no matter how hard I try, I couldn't succeed. Although I get quite some materials in youtube and google for annuity ratio, nothing gives me a straight forward equation for a similar example.

Below are the boundary conditions:
Tenure of insuance coverage is known, Maximum possible return which is at the first insurance of coverage is known and annuity percentage is known.

Can someone in this group help me to find the equation pl.?
 
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Have you tried plotting these values? Try both column S and T versus the age.
Hint, you don't need to key in every value.

Another hint: I left out the value at 55.

Desmos.com has an interactive linear regression calculator that can help figure out a formula.
 
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Better yet, find a life table and figure out what is the expected value. This should be a cheap policy as the payout is small and declining. Also ask yourself what are you insuring? (It’s not your life). Is this enough of a payout for your family to replace your income?

Also is there a medical exam? If not, and your health is good, you will be overpaying.
 
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Looking at this again, this almost looks like a life insurance policy that you might get on a loan. If the borrower dies, then the balance of the loan is paid off - hence the declining payout.
 
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scottdave said:
The amounts in your column T are a geometric sequence with ratio = 1.06

There is a formula for the partial sums of the values of a geometric sequence. See this for more information:
https://www.mathsisfun.com/algebra/sequences-sums-geometric.html
Sorry for a very late reply and I really appreciate your efforts to help me!
I actually started form the"mathsisfun" page. However I still couldn't figure out the sequence.
Also this morning, after seeing your first reply, I tried desmos also. Though a parabola equation based regression was close, it was not the exact equation.
 
k.udhay said:
Sorry for a very late reply and I really appreciate your efforts to help me!
I actually started form the"mathsisfun" page. However I still couldn't figure out the sequence.
Also this morning, after seeing your first reply, I tried desmos also. Though a parabola equation based regression was close, it was not the exact equation.
As @scottdave mentionee before, it just looks like the policy self-finances a level premium at a 6% interest rate
 
BWV said:
As @scottdave mentionee before, it just looks like the policy self-finances a level premium at a 6% interest rate
Might be true, but where can I find this formula? Thank you for helping me.
 
k.udhay said:
Might be true, but where can I find this formula? Thank you for helping me.
Death benefit at year n=345000- sum(4363.87*1.06^(n-1)) from 1 to n?
 
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  • #10
BWV said:
Death benefit at year n=345000- sum(4363.87*1.06^(n-1)) from 1 to n?
Ah, but the number 4363.87 should not be a part of the equation. Like I said, I would like to use a formula with which I can change the interest rate, years of coverage etc.
 
  • #11
k.udhay said:
Ah, but the number 4363.87 should not be a part of the equation. Like I said, I would like to use a formula with which I can change the interest rate, years of coverage etc.
But that includes the mortality charge - do get the number you would need the ins company’s mortality table and how they compute a level term premium from it
 

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