Public debt/Addendum

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https://en.citizendium.org/wiki/index.php?title=Public_debt/Addendum&printable=yes
This addendum is a continuation of the article Public debt.
ΔD = (D + F + Dr)/{Y(1 + r)} - D/Y

let 1/{Y(1 + g)} = A then:

= A(D + F + Dr) - D/Y
= A( D + F + Dr  - D/AY)
= A( D + F + Dr - D - Dg)

substituting for A:

= {F + D(r - g)}/{Y(1 + g)}

or, approximately

= {F + D(r - g)
= F/Y +(r - g)D/Y

putting F/Y = f  andD/Y = d:

= f + d(r - g)
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