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.