Savings Calculator with Monthly Deposit

Compound Interest Formula with Monthly Deposits:

\[ A = P \times (1 + \frac{r}{365})^{365 \times t} + \sum \left( C \times (1 + \frac{r}{365})^{365 \times (t - Ct)} \right) \]

Initial Principal (P):

Annual Interest Rate (r):

Time Period (t):

years

Monthly Deposit (C):

Final Amount (A):

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1. What is the Savings Calculator with Monthly Deposits?

This calculator computes the future value of savings with both an initial principal and regular monthly deposits, using daily compounding interest. It's useful for planning long-term savings goals like retirement or education funds.

2. How Does the Calculator Work?

The calculator uses the compound interest formula with monthly deposits:

\[ A = P \times (1 + \frac{r}{365})^{365 \times t} + \sum \left( C \times (1 + \frac{r}{365})^{365 \times (t - Ct)} \right) \]

Where:

$ A $ — Final amount ($)
$ P $ — Initial principal ($)
$ r $ — Annual interest rate (decimal)
$ t $ — Time in years
$ C $ — Monthly contribution ($)
$ Ct $ — Time since contribution was made (years)

Explanation: The formula accounts for daily compounding of both the initial principal and each monthly deposit based on how long each deposit has been invested.

3. Importance of Compound Interest

Details: Compound interest allows your money to grow exponentially over time. Regular monthly deposits significantly boost the final amount due to the power of compounding.

4. Using the Calculator

Tips: Enter the initial amount you plan to invest, the annual interest rate (e.g., 3.5 for 3.5%), the number of years you plan to save, and your monthly contribution amount.

5. Frequently Asked Questions (FAQ)

Q1: How often is interest compounded in this calculator?
A: Interest is compounded daily (365 times per year) for maximum accuracy.

Q2: Does this account for taxes on interest earned?
A: No, this calculator shows gross returns before taxes. Actual after-tax returns may be lower.

Q3: What's the benefit of monthly deposits vs. lump sum?
A: Monthly deposits allow dollar-cost averaging and take advantage of compounding over different time periods.

Q4: Can I use this for irregular deposit amounts?
A: This calculator assumes fixed monthly deposits. For irregular amounts, you'd need a more complex calculation.

Q5: How accurate is this for high-yield savings accounts?
A: Very accurate for accounts with fixed APY. For variable-rate accounts, results are estimates based on current rate.