Calculation methods
How our estimates are calculated
Our calculators use fixed-rate scenarios and separate principal or deposits from estimated interest. The formulas differ according to the question: amortize a loan, value a CD at maturity, project a plan forward, or solve backwards from a savings goal.
Compound interest inputs
Starting amount is the balance at the beginning of year one. Deposit each period is added monthly, quarterly, twice yearly, or yearly. A zero deposit models growth of the starting amount alone.
Annual interest rate is a nominal rate held constant throughout the projection. Compounding frequency says how often interest is added; it can differ from the deposit frequency. Deposits can arrive at the beginning or end of each deposit period. Beginning-of-period deposits have one extra period of assumed growth.
Compound interest calculation
For each deposit period, the calculator turns the nominal annual rate into an effective period rate:
period rate = (1 + annual rate / compounding periods per year)^(compounding periods per year / deposit periods per year) - 1
It applies that growth to the current balance and adds the scheduled deposit before or after growth according to your selection. The next period starts with the new balance, so prior interest can itself earn interest. The displayed interest is the ending balance minus the starting amount and all deposits.
When compounding and deposits follow different schedules, the model distributes effective growth evenly across deposit periods. It does not use calendar dates or an institution's specific accrual rules.
A compound interest example you can check
Enter $1,000 to start, $0 in deposits, 5% annually, two years, and annual compounding. After year one, the balance is $1,050. After year two, the next 5% is applied to $1,050, giving $1,102.50. Of that total, $102.50 is interest. This matches the Consumer Financial Protection Bureau's compound-interest example.
Savings goal calculation
The savings goal calculator treats the entered APY as an effective annual yield. It converts that yield into an effective rate for monthly, biweekly, or weekly deposits:
period rate = (1 + APY)^(1 / deposit periods per year) - 1
When you provide a deadline, it first grows the current savings to that point and then solves the future-value-of-an-annuity formula for the recurring deposit. The answer is rounded up to the nearest cent. When you provide the recurring deposit, it solves for the first period in which the projected balance meets or exceeds the goal.
A deposit made at the beginning of a period receives one additional period of assumed interest. Monthly, biweekly, and weekly periods are modeled as equal parts of a year rather than exact calendar dates.
A savings goal example you can check
Set a $10,000 goal, $0 already saved, 0% APY, and a one-year monthly deadline. The gap is divided across 12 deposits. Because $10,000 ÷ 12 is $833.333…, the calculator rounds up to $833.34. Twelve deposits total $10,000.08, ensuring the displayed plan does not finish below the goal.
CD maturity calculation
The CD calculator treats APY as the effective annual return, including compounding. It uses maturity value = opening deposit × (1 + APY)^(term months / 12). A $10,000 CD held for 12 months at 4% APY reaches $10,400, including $400 of interest.
Loan payment and amortization calculation
The loan calculator models a fixed-rate, fully amortizing loan. It converts APR to a monthly rate and uses payment = principal × monthly rate / (1 − (1 + monthly rate)^−months). At 0% interest, the payment is principal divided by the number of months.
Each month, interest equals the remaining balance multiplied by the monthly rate. The required payment first covers that interest, and the rest reduces principal. An optional extra amount is applied to principal in the model. The final payment is capped at the balance plus that month's interest.
For example, $10,000 borrowed for 60 months at 6% APR produces a required payment of about $193.33 and approximately $1,599.68 in total interest, subject to cent-level lender rounding.
What the estimates leave out
The saving projections assume the same rate and deposit amount for the whole period. The loan model assumes a fixed APR, monthly payments, and extra payments applied to principal. It excludes origination and late fees, taxes, insurance, daily interest, prepayment penalties, changing rates, and lender-specific rules. Every result is an educational scenario, not a forecast, account statement, loan offer, or recommendation.
Dollar inputs must be in whole cents. The calculators keep precision during growth and round amounts for display, but do not model a bank's transaction-by-transaction rounding. They refuse a projected balance above $1 trillion rather than display cents beyond the reliable range.
For independent tools with different assumptions, compare a scenario with Investor.gov's Compound Interest Calculator or Savings Goal Calculator.