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
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
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.
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.