Sequence formula needed - Keyword --> annuity

[k.udhay]

TL;DR Summary

Find out the equation of sequencing numbers; Annuity calculation

Below is a screenshot of an insurance policy:

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.?

 

[scottdave]

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.

 

[BWV]

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.

 

[scottdave]

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.

 

[scottdave]

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

 

[k.udhay]

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.

 

[BWV]

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

 

[k.udhay]

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.

 

[BWV]

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?

 

[k.udhay]

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.

 

[BWV]

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