1) Cumulative Interest Calculator (Savings & Loans)

Use this free cumulative interest calculator to see cumulative interest earned on savings or paid on loans. It handles APR↔APY, compounding (daily, monthly, quarterly, etc.), recurring contributions, deposit timing (begin vs end of period), taxes on interest, fees, inflation, and biweekly vs monthly loan payments. Export tables to CSV and share your scenario with a link.

2) Who Is This For?

• Savers comparing bank APYs, CDs, and automatic deposits
• Borrowers planning mortgages, car loans, or student loans (with extra payments)
• Anyone who wants to see “what am I actually earning or paying in interest over time?”
• Educators and creators who need an accurate amortization/compound model with CSV export

3) Quick Guide: How to Use the Cumulative Interest Calculator

3.1) Savings (Interest Earned)

1. Select the Savings tab and enter your Initial deposit.
2. Choose APY (or APR) and your Compounding frequency.
3. (Optional) Add a Recurring contribution and choose deposit timing: Beginning (e.g., paycheck day) or End of period.
4. Open Advanced Options to include taxes on interest, monthly flat fees, annual fee %, and inflation (for a “real” ending balance).
5. Read the tiles for Ending Balance, Total Contributions, and Cumulative Interest. Drag the slider to see cumulative interest up to any month (e.g., month 24).
6. Use Copy data for CSV or Copy link to share your exact inputs.

3.2) Loans (Interest Paid)

1. Select the Loans tab in the cumulative interest calculator and enter your Loan amount, APR, Years, and Payment frequency (Monthly or Biweekly).
2. (Optional) Set a fixed Extra payment per period to see payoff acceleration.
3. Drag the slider to see cumulative interest paid from period 1 up to your chosen period (e.g., first 60 payments).
4. Export the amortization table with Copy data or share with Copy link.

4) Practical Examples (With Real Numbers)

4.1) Savings Example: Automatic Deposits Into a High-Yield Account

• Scenario: $10,000 initial deposit, 5% APY, monthly compounding, $100 monthly contribution for 10 years, deposits at end of month.
• Result: Ending balance ≈ $31,725; Total contributions = $12,000; Cumulative interest ≈ $9,725.
• Tip: Switch Deposit timing = Beginning to reflect payday deposits; ending balance rises slightly (≈ $31,788) because each contribution earns one extra month of interest.

4.2) “Real” Growth After Taxes and Inflation

• Start: Use the same savings scenario in the cumulative interest calculator. In Advanced Options, set your estimated tax on interest and inflation rate.
• Result: The calculator shows a Real end balance (inflation-adjusted) so you compare purchasing power, not just nominal dollars.

4.3) Car Loan Example: Monthly Payments

• Scenario: $30,000 car, 6.0% APR, 5 years, monthly payments, no extra payments.
• Result: Payment ≈ $579.98/month; Total of payments ≈ $34,799; Cumulative interest ≈ $4,799.
• Tip: Add $50 extra/month: watch total interest drop and payoff speed up.

4.4) Mortgage Example: Biweekly vs Monthly

• Scenario: $300,000 mortgage, 6.5% APR, 30 years.
• Monthly: Payment ≈ $1,896; Total of payments ≈ $682,633; Cumulative interest ≈ $382,633.
• Biweekly: Payment per period ≈ $874.76; Total of payments ≈ $682,312; Cumulative interest ≈ $382,312.
• Note: Biweekly often reduces interest because you effectively make ~1 extra monthly payment per year.

5) Formulas Used in the Cumulative Interest Calculator (What’s Happening Behind the Scenes)

5.1) Rates & Conversions

Quick formulas

APY from APR (compounded n times/year):

APY = (1 + APR / n)n − 1

APR from APY:

APR = n × ( (1 + APY)1/n − 1 )

Equivalent monthly rate from APR and compounding n:

rmonth = (1 + APR / n)n/12 − 1

5.2) Savings Growth

Future value formulas

Without contributions (effective annual rate r_eff):

FV = Principal × (1 + r_eff)years

With periodic contributions PMT at frequency m per year (effective period rate i):

FV = Principal × (1 + i)m·years + PMT × [ ((1 + i)m·years − 1) / i ]

Beginning-of-period deposits: multiply the contribution term by (1 + i).

Taxes on interest:

Reduce each period’s interest by (1 − tax_rate).

Fees:

Subtract flat monthly fees after interest; apply annual fee % as an equivalent monthly rate.

Inflation-adjusted (real) ending balance:

Real FV = Nominal FV / (1 + inflation)years

Note

Because taxes/fees/inflation interact over time, the calculator runs a precise month-by-month simulation rather than a single closed-form.

5.3) Loan Amortization in the Cumulative Interest Calculator

Payment & amortization formulas

Payment per period (annuity), where i = APR / payments_per_year and N = years × payments_per_year:

PMT = L × i / ( 1 − (1 + i)−N )

i = APR / payments_per_year  •  N = years × payments_per_year

Each period:

Interest = Balance × i

Principal = PMT − Interest

Balance reduces by Principal (plus any extra payment).

Cumulative interest

Sum of period interest up to the selected period.

6) APR vs APY (Clear Difference)

• APR (Annual Percentage Rate): nominal yearly rate, does not include the effect of compounding.
• APY (Annual Percentage Yield): includes compounding and shows the actual year-over-year growth on savings.
• Rule of thumb: For savings, compare APY. For loans, APR is typically quoted; your effective cost also depends on payment frequency and fees.

7) Cumulative Interest vs Compound Interest

• Compound interest is the mechanism: interest accrues on principal plus previously earned interest (savings) or on the current balance (loans).
• Cumulative interest is the total amount of interest accumulated over time, either total interest earned (savings) or total interest paid (loans).
• In this cumulative interest calculator, the Cumulative interest tiles show the running total up to the month/period you select.

8) Best Practices & Tips

Use the slider to answer questions like: “How much interest in the first 24 months?” or “What if I stop after year 3?”

For savings, set APY and choose the bank’s compounding (often daily or monthly). Add contributions and use Beginning timing if you deposit on payday.

Turn on taxes/fees only if they apply; otherwise leave them at zero for clean comparisons.

For loans, test biweekly vs monthly and try a small, fixed extra payment, sustained extras often outperform one-time lump sums.

9. Disclaimer (important)

This cumulative interest calculator is for education and planning only and does not provide financial, tax, or investment advice. Results are estimates based on your inputs and general assumptions. Always verify figures with your financial institution and consider consulting a qualified professional for advice tailored to your situation.