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Jan Karman
Middelburg (Neth)

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Jan Karman
Last revised: February 2021

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Retiring together?
Challenges for dual earners

The proportion of dual earners among adults aged 60 years and over is increasing. In the Netherlands, we find that many older dual earners would like to retire at the same time, but are put off by the financial consequences. Due to the gradual increase of the public pension age, younger partners will have to continue working long after the older partner has retired. See more

Source: Demos/Nederlands Interuniversitair Demografisch Instituut


Otium cum dignitate

Middelburg - The Netherlands

The Price of Bonds
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Valuation of bond prices is a big thing at Wall Street and at investment departments of every institutional investor, like insurance companies, pension funds, etc. Buying bonds entitles one to receiving the principal at a given date, plus the contractual interest payments, i.e. coupons.
This, being called the cashflow, has a value, depending on quite a few parameters. which include the principal, the contractual interest rate, frequency of coupons (usually 2), redemption scheme (at once, linear, annuity, etc), date of closure, date of (starting) redemption and maturity date.
The technique of determination of prices of bonds is known as "Mathematics of Finance" or "Mathematics of Investment"
The general formula x = H + iL can be considered from different view points:
  (1) sum of present values of redemption and intrest (as the formula shows)
  (2) price as deviation from par, i.e. the present value
       of the difference between interest rate and yield
  (3) price related to a non-repayable loan; here the
       formulae will always show up as: i/r + ..., since i/r is
       the price of a non-repayable loan.
Type (3) is the most practical one for calculations, since it only needs flat annuities, rather than incremental or decremental ones, like needed in Type (1) and (2), and which I used for the functions in the K-script. Further it's an interesting (mathematical) exercise to express a given formula from one type into another.
E.g. the price of an annuity is easy: an(i)/an(r). But expressing this in one of type (1) for example, means headaches!

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Actuarial & financial applications:
 Actuarial Factors
 Annuity Loan
 Graduation of Mortality
 Profit & Loss in Stocks
 The Price of Bonds
 Afronding van sterftetafels
 Ausgleichung von Sterbetafeln
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