D.W. Simpson Worldwide Actuarial Recruitment Life Health Pension Casualty US Asia Australia Europe Salary Apply Ezra Penland Actuarial Recruiters Top Actuary Jobs Salary Surveys Apply Bios Casualty Health Life Pension Pauline Reimer, ASA, MAAA Pryor AssociatesActuarial Openings: Life, P&C, Health, Pensions, Finance Advertise Here Contact us at actuary@actuary.com or 770-425-8576Reach top actuarial professionals

1. ## ASM Perpetuity Confusion

Hello all,

When I am dealing with m-thy payment perpetuities, (pg. 177 11th edition) if anyone has it.

The book keeps saying that the PV formula, for say, a m-thly perpetuity-immediate with payments of 1/m every m-th period and 1 per year is one divided by i^(m). However, it seems as if the numerical answers use one divided by the m-thy effective rate.

For example, if we are looking at a perpetuity-immediate with payments of 1/12 per month forever. Then, we would want to do one divided by the effective monthly interest rate to find the PV of this annuity. However, it looks like the manual is saying to use the nominal monthly interest rate?

I just wanted to clear this up because in many equations in this manual, i^(m) or d^(m) is used and I was under the assumption that these were nominal rates of interest and discount.

Thanks all.  Reply With Quote

2. Originally Posted by MHailJ Hello all,

When I am dealing with m-thy payment perpetuities, (pg. 177 11th edition) if anyone has it.

The book keeps saying that the PV formula, for say, a m-thly perpetuity-immediate with payments of 1/m every m-th period and 1 per year is one divided by i^(m). However, it seems as if the numerical answers use one divided by the m-thy effective rate.

For example, if we are looking at a perpetuity-immediate with payments of 1/12 per month forever. Then, we would want to do one divided by the effective monthly interest rate to find the PV of this annuity. However, it looks like the manual is saying to use the nominal monthly interest rate?

I just wanted to clear this up because in many equations in this manual, i^(m) or d^(m) is used and I was under the assumption that these were nominal rates of interest and discount.

Thanks all.
I did not use ASM for FM, but I don't think 11 edition would have any major issue on important concepts.

PV of yearly perpetuity immediate of 1 is 1/i where i is the effective interest rate.

PV of m-thly perpetuity immediate of 1 is 1/i^(m) where i^(m) is the m-thly effective interest rate.  Reply With Quote

3. Originally Posted by BeanCounter I did not use ASM for FM, but I don't think 11 edition would have any major issue on important concepts.

PV of yearly perpetuity immediate of 1 is 1/i where i is the effective interest rate.

PV of m-thly perpetuity immediate of 1 is 1/i^(m) where i^(m) is the m-thly effective interest rate.
That is what I thought...but then, we also see in the manual;

(1+i) = (1+i^(m)/m)^m

where i is the annual effective and i^(m) is the nominal m-thy rate...

And they use 1/i^(m) in the manual - where I believe it should be 1/(i^(m)/m)  Reply With Quote