4 ms·
Pretty sure it's not an approximation, at least for interest rates compounded continuously. The real interest rate is simply the nominal interest rate minus in
by nostrademons 3y ago
Pretty sure it's not an approximation, at least for interest rates compounded continuously. The real interest rate is simply the nominal interest rate minus inflation. The algebra is
e^(realt) = e^(nominalt) / e^(inflationt). Left side is your compounded real gains, first factor is on the right is your compounded nominal gains, and the divisor is the cumulative price rise to go from nominal to real terms.
e^(real t) = e^(nominalt - inflationt), by quotient rule for exponents.
e^(real * t) = e^(t * (nominal - inflation)), factoring out t.
real * t = t * (nominal - inflation), taking natural log of both sides
real = nominal - inflation, dividing by t
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- yorwba 3y agoInterest rate and inflation are usually expressed as e^(exponent * one year) - 1, so to get from 45% to the exponent you need to add one and take the logarithm, giving 0.37
- rightbyte 3y agoHmm ... my heads hurt doing math ... so not: e^(real x t) = e^(nominal x t) - e^(inflation x t) ? Like, you have 1$ in the bank that can buy 1 foo widget. After a year the foo widget is 1.65$ and you have 1.45$, missing 12% of the sum you need. I.e the same thing as having no inflation and a 12% tax. Your definition seem to break down when "nominal - inflation" is bigger than -100%. Or what would -110% real interest mean?
- deleted 3y ago[deleted]
- randomdata 3y ago> I.e the same thing as having no inflation and a 12% tax. If we assume there is no inflation, then after one year the foo widget is still $1 [1] and you have 80¢ [2] – a 20% tax. [1] $1.65 - $0.65 = $1.00 [2] $1.45 - $0.65 = $0.80