Savings Calculator Compounded Daily

Daily Compounding Formula:

\[ FV = P \times (1 + r / 365)^{(365 \times t)} + PMT \times \left[\frac{(1 + r / 365)^{(365 \times t)} - 1}{r / 365}\right] \]

Initial Principal (P):

Annual Interest Rate (r):

decimal

Time (t):

years

Periodic Payment (PMT):

$ per period

Future Value (FV):

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1. What is the Daily Compounding Savings Formula?

The daily compounding formula calculates the future value of an investment with daily interest compounding and regular contributions. It accounts for both the initial principal and periodic payments growing at a daily compounded rate.

2. How Does the Calculator Work?

The calculator uses the daily compounding formula:

\[ FV = P \times (1 + r / 365)^{(365 \times t)} + PMT \times \left[\frac{(1 + r / 365)^{(365 \times t)} - 1}{r / 365}\right] \]

Where:

$ FV $ — Future Value ($)
$ P $ — Initial Principal ($)
$ r $ — Annual Interest Rate (decimal)
$ t $ — Time in years
$ PMT $ — Periodic Payment ($ per period)

Explanation: The formula calculates how much your investment will be worth in the future with daily compounding interest and regular contributions.

3. Importance of Daily Compounding

Details: Daily compounding allows your money to grow faster than less frequent compounding periods. The interest earned each day gets added to the principal, which then earns more interest the next day, creating a snowball effect.

4. Using the Calculator

Tips: Enter initial principal in dollars, annual interest rate as a decimal (e.g., 0.05 for 5%), time in years, and periodic payment in dollars. All values must be valid (principal ≥ 0, rate ≥ 0, time > 0, payment ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: How does daily compounding compare to monthly or annual compounding?
A: Daily compounding typically yields higher returns than less frequent compounding because interest is calculated and added to the principal more frequently.

Q2: What's the difference between APR and APY?
A: APR (Annual Percentage Rate) doesn't account for compounding, while APY (Annual Percentage Yield) does. APY will be higher than APR with frequent compounding.

Q3: How often should I make contributions for maximum growth?
A: More frequent contributions (daily, weekly) will maximize growth due to more time in the market, though monthly is most common for practical purposes.

Q4: Are there any limitations to this calculation?
A: This assumes a fixed interest rate and consistent contributions. Real-world rates may fluctuate, and contributions may vary over time.

Q5: How does this apply to different types of savings accounts?
A: This formula works for any investment with daily compounding, including high-yield savings accounts, certificates of deposit, and some investment accounts.