Value of savings in the future
Where
S = amount of savings today
A = annual additions to savings
n = number of years of saving
r = assumed rate of return
V = value of savings in n years
Amount of savings needed today
Where
S = amount of savings today
A = annual additions to savings
n = number of years of saving
r = assumed rate of return
V = value of savings in n years
Amount of annual savings needed
Where
S = amount of savings today
A = annual additions to savings
n = number of years of saving
r = assumed rate of return
V = value of savings in n years
Rate of return required to reach a future savings goal
This cannot be done with a formula. The value of r must be found using an iterative technique. There are several methods of doing this. We use a hybrid of the Newton-Raphson and bisection methods described by Press, Teukolsky, Vetterling, and Flannery on pp. 366-367 in Numerical Recipes in C (1999, Cambridge University Press).