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Savings Calculator

Formula

The formula to calculate the initial deposit required to accumulate a certain future value with compound interest is:

$\text{Amount} = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

$\text{Amount}$ is the future value you want to accumulate
$P$ is the initial deposit
$r$ is the annual interest rate
$n$ is the number of times the interest is compounded per year (for this example, we assume it is compounded annually, so $n = 1$ )
$t$ is the number of years

Assuming you want to accumulate $5000 in 7 years with an annual interest rate of 5%, you would use the formula as follows:

$5000 = P \left(1 + \frac{0.05}{1}\right)^{1 \times 7}$

Rearranging to solve for $P$ :

$P = \frac{5000}{\left(1 + 0.05\right)^7}$

So, the initial deposit $P$ is:

$P = \frac{5000}{1.05^7} \approx 3553.41$

Therefore, you need to deposit approximately $3553.41 to accumulate $5000 in 7 years with a 5% annual interest rate.