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If an annuity pays 4800 annually with a 2% increase per year or has an option of 6000 annually, how many years will the total amount paid is equal in both options

Each year is 4800 + 4800 x 1.02 + 4800 x 1.02^2.... vs 6000 + 6000 + 6000...

tom murphy
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1 Answers1

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With this calculation, since there is no interest rate or anything of that sort, I am assuming future value doesn't matter and we are just solving for a straight value.

Note first that $\sum_{i=0}^{n-1}ar^i=a\left(\frac{1-r^n}{1-r}\right)$. With this we see that we are trying to solve $$\sum_{i=0}^{n-1}48000(1.02)^i=6000n$$

But this can be rewritten as $$4800\left(\frac{1-(1.02)^n}{1-(1.02)}\right)=6000n$$ Now just solve for $n$

Kamster
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