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I have to calculate the monthly value I have to save with 4.5 % interest to get € 529411 in 35 years.

As I know, it is about € 520 but I need a formula to integrate it into my software.

Thank you

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    Is the interest only compounded annually? Or monthly?2011-11-12

2 Answers 2

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The accumulated future worth $F$ at the end of $n=35\times 12$ equal deposits$^1$ $A$ compounded monthly at an interest rate per month $i=0.045/12$ is the sum

$F=\sum_{k=1}^{n}A(1+i)^{n-k}=A\frac{(1+i)^{n}-1}{i}.$

So

$A=F\dfrac{i}{(1+i)^{n}-1}=529411\dfrac{0.045/12}{(1+\dfrac{0.045}{12} )^{35\times 12}-1}=520.18.$

$^1$ Each deposit is assumed to be made at the end of each month.

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    @ShaneORourke: I used the assumption of end-of-period compounding by two reasons: 1) it is used in *Engineering Economics* by Riggs, Bedworth and Randhawa in the derivation of the sinking fund factor $A/F$. 2) It agrees with the numerical value indicated by OP.2011-11-12
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The formula is

$\text{Monthly payment} = \dfrac{\text{Monthly interest}}{(1+\text{Monthly interest})^{\text{Duration}}-1} \times \text{End capital}$

If you compute the monthly interest as $0.045/12$, you'll get $520.18$ as the end result.

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    Yeah, forgot it.2011-11-12