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the question is asking me to Prove that $d_n$ is constant in the case of compound interest.

What I know so far and have tried is the formula for compound interest is $a(t)=(1+i)^t$ and I think that $d_n$ is possibly supposed to represent the discount maybe. But I there is no $d_n$ in the formula for compound interest so I am confused on how I am supposed to prove this.

Harper Jeffrey
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  • $d_n$ is the initial capital? – user Dec 03 '17 at 19:11
  • Have a look in your papers and see what $d_n$ means. This is the simplest way. – callculus42 Dec 03 '17 at 19:15
  • $$Amount= P(1+ \frac{R}{100})^t $$ . There is no discount term anywhere. Check your question again – Your IDE Dec 03 '17 at 19:17
  • the question in my text only says "prove that $d_n$ is constant in the case of compound interest" there is no other information in the question. That is all I have been able to figure out – Harper Jeffrey Dec 03 '17 at 19:32
  • some of the other formulas I have found with $d_n$ are: $d_n$= a(n)-a(n-1) / a(n)$ which is the formula for the effective rate of discount in the nth year – Harper Jeffrey Dec 03 '17 at 19:34

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$$ a(n) = P (1+i)^n $$

$$ d_n = \frac{P (1+i)^n -P (1+i)^{n-1} }{P (1+i)^n } = 1-(1+i)^{-1} $$ which does not depend on $n$

WW1
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