What This Calculator Does
This tool projects how much a savings or investment account will be worth after a given number of years when you start with an initial deposit and add the same amount every year. It combines compound growth on your starting balance with the future value of a series of equal annual contributions, giving you a single, realistic estimate of your ending balance.
How to Use It
Enter your initial deposit (\(P\)), the amount you plan to add each year (\(D\)), the annual interest rate as a percentage, and how many years you want to project. The calculator returns your final balance, the total amount you contributed, and the interest earned on top of those contributions.
The Formula Explained
The balance is calculated as $$A = P(1+r)^{t} + D \times \frac{(1+r)^{t} - 1}{r}.$$ The first term grows your initial deposit by compound interest. The second term is the future value of an ordinary annuity — it assumes each annual addition is made at the end of the year and then compounds for the remaining years. The rate \(r\) is the decimal form of your percentage (\(5\% = 0.05\)). If the rate is zero, the formula simplifies to \(A = P + D \times t\).
Worked Example
Suppose you deposit $1,000, add $1,000 at the end of each year, earn 5% annually, and save for 10 years. The growth factor is \(1.05^{10} \approx 1.62889\). The initial deposit grows to about $1,628.89. The annuity portion is \(1{,}000 \times \frac{1.62889 - 1}{0.05} \approx \$12{,}577.89\). Adding them gives a final balance of about $14,206.79, of which $11,000 was contributed and roughly $3,206.79 is interest.
FAQ
Are additions made at the start or end of the year? This calculator uses end-of-year additions (an ordinary annuity), so the latest contribution does not earn interest in its final year.
Can I use a 0% rate? Yes. With no interest, the balance equals your initial deposit plus all annual additions.
Does this account for inflation or taxes? No. Results are nominal pre-tax figures; adjust the rate downward if you want a real (inflation-adjusted) estimate.
