How to find the amount to added every month or year to get the required amount after certain years?

Question

I want to do a Java application for which after giving the current savings, and the rate of interest and and required amount after specified no of years, it has to show how much a person has to earn a month or year to achieve his target. I'm aware of the formula $$\text{present value}={\text{future value} \over (1+\text{interest rate})^{\text{no. of years}}}$$ Now after getting present value, should I divide present value by no. of months in those years, to get the amount he has to invest per month ?

Answer 1

The formula you need is the future value of an ordinary annuity:

$$F=R \times \frac{(1+i)^n-1}{i}$$where F is the value at the time of the last payment, R is the size of the regular payment, i is the interest rate per payment period and n is the number of regular payments.

The compounding period of the interest rate must match the payment period...

REVISED ANSWER: Assume you start with B dollars, and wish to accumulate a total of C dollars after n years, making annual deposits of R dollars, and earning an annual rate of i per year as you go.

The original amount will grow, all by itself, to $B'$ at the end of the payments:

$$B'=B \times (1+i)^n $$Assuming that this is less than your target of C dollars, the regular payments must make up the difference of $C-B'$. Re-arranging the formula for the future value of an annuity: $$R=(C-B') \times \frac{i}{(1+i)^n-1}$$

Answer 2

Take a look at the geometric mean. It can be used to find average growth rates. From the average rate and the given amount you can easily derive the average increase per time period.

EDIT Maybe you're looking for this:

$$(1+\text{interest rate})^{\text{no. of years}}=\frac{\text{future value}} {\text{present value}}$$

$$\text{interest rate}=\sqrt[\leftroot{-2}\uproot{2}\text{no. of years}]{\frac{\text{future value}} {\text{present value}}} - 1$$