Interest Calculator

Put $10,000 in an account paying 5% a year for 10 years and the result depends entirely on how the interest is calculated. With simple interest, you earn a flat $500 every year, or $5,000 total, ending at $15,000. With compound interest (compounded monthly), each month's interest also earns interest, so you finish with about $16,470 - roughly $6,470 in interest, or about $1,470 more than simple interest. This interest calculator shows both numbers side by side so you can see the gap for your own inputs.

The two formulas

Simple interest is calculated only on the original principal:

Compound interest is calculated on the principal plus all interest earned so far:

Here P is the principal, r is the annual rate as a decimal (5% = 0.05), t is the time in years, and m is the number of compounding periods per year (12 for monthly, 365 for daily). The interest earned with compounding is simply FV − P.

Why compound interest pulls ahead

With simple interest the balance rises in a straight line - the same dollar amount every period. With compound interest the growth curve bends upward because you earn "interest on interest." In the early years the two are close, but the gap widens the longer your money stays invested. Over 30 years at a typical rate, compounding can roughly double the interest you'd earn under simple interest. This is the core reason long-term savers and investors prioritize starting early.

How compounding frequency changes the result

The more often interest compounds, the more you earn, because interest starts earning interest sooner. Going from annual to monthly compounding gives a meaningful bump; going from monthly to daily adds only a little more. That is why banks often advertise an APY (annual percentage yield), which already bakes in the effect of compounding, while a stated nominal rate does not. Enter the plain annual rate above and pick a frequency to see how it shifts the final balance.

When each type applies

• Simple interest: common on some short-term and auto loans, certain bonds, and many fixed-payment consumer loans.
• Compound interest: standard on savings accounts, CDs, money-market accounts, and most investment growth - and also on credit-card balances you carry.
• Either way: a higher rate and a longer time horizon are the biggest levers. Compounding frequency matters, but less than rate and time.

If you only care about one side of the comparison, a focused tool is cleaner: the Compound Interest Calculator breaks down growth on savings and investments, while the Simple Interest Calculator handles flat interest on a loan or note.

How to use this calculator

You only need four inputs to compare both methods. Work through the fields in order:

1. Principal: enter the starting amount - the lump sum you are depositing or borrowing.
2. Annual interest rate: type the rate as a percent (for example 5, not 0.05). The calculator converts it to a decimal for the formulas.
3. Time: set how many years the money stays invested or borrowed. Longer horizons widen the gap between simple and compound.
4. Compounding frequency: choose annual, semi-annual, quarterly, monthly, or daily. This only affects the compound side; simple interest ignores frequency.

The result updates instantly. Read the interest earned and final balance for both methods, note the dollar difference between them, and scroll the year-by-year table to watch the compound balance bend away from the straight simple-interest line.

A second worked example: $5,000 at 7% for 20 years

Suppose you put $5,000 into an account paying 7% for 20 years. With simple interest, you earn $5,000 × 0.07 × 20 = $7,000, ending at $12,000. With compound interest at the same rate, compounded monthly, the balance grows to roughly $20,200 - about $15,200 in interest, or more than double what simple interest would pay. The only thing that changed is whether interest is allowed to earn interest. This is why the same rate over a long horizon can produce wildly different outcomes depending on the method.

Shorten the same example to 5 years and the gap nearly disappears: simple interest pays $1,750 while monthly compounding pays about $2,089 - a difference of only $339. Compounding is a slow start and a fast finish, which is the whole argument for leaving money invested.

Nominal rate, effective yield, and APY

The number you type is the nominal annual rate - the headline figure before compounding is applied. Once interest compounds more than once a year, the amount you actually earn over twelve months is the effective annual rate (EAR), also marketed as APY on savings products. For example, a 5% nominal rate compounded monthly produces an EAR of about 5.12%; compounded daily it is about 5.13%. The formula is EAR = (1 + r ÷ m)^m − 1. When you compare two accounts, line up their APYs - not their nominal rates - because APY already reflects how often each one compounds. If you instead know your target balance and want to back out the rate it would take to get there, the Interest Rate Calculator solves for r directly.

Key terms explained

• Principal: the original amount deposited or borrowed, before any interest is added.
• Interest: the cost of borrowing money, or the reward for lending or saving it, expressed as a percentage of the principal per year.
• Compounding period (m): how often interest is calculated and added to the balance - annually (m = 1) up to daily (m = 365).
• Future value (FV): the final balance after interest, which the compound formula solves for directly.
• APY / effective annual rate: the true yearly return once compounding is included; always greater than or equal to the nominal rate.
• APR: on loans, the annual cost of borrowing including certain fees - the mirror image of APY for savers.

The Rule of 72: a quick mental check

To estimate how long compound interest takes to double your money, divide 72 by the annual rate. At 6% your money roughly doubles in 72 ÷ 6 = 12 years; at 8% it doubles in about 9 years; at 4% it takes about 18 years. The Rule of 72 is an approximation that works best for rates between roughly 4% and 12%, but it is a fast sanity check against the calculator's exact output and shows why even small rate differences compound into large gaps over decades.

Who this calculator is for

This tool is built for anyone who needs to see, in plain dollars, how a single amount grows or costs over time. That includes:

• Savers comparing what a CD or high-yield savings account will pay over a fixed term, and checking whether the quoted APY matches the nominal rate plus compounding.
• Students learning the math behind the two formulas and wanting a side-by-side answer to "how different are they, really?"
• New investors building intuition for why a longer time horizon matters far more than chasing a slightly higher rate.
• Borrowers sizing up the interest on a simple-interest loan or note before signing, or seeing how a carried balance compounds against them.
• Planners stress-testing a goal: enter a principal and rate to see whether a lump sum will reach a target by a certain year.

How to make the number bigger

If the final balance is smaller than you hoped, three levers move it - in roughly this order of impact:

• Add time. Because compounding accelerates, extra years late in the timeline add the most. Starting five years earlier often beats a full extra percentage point of rate.
• Raise the rate. Shopping for a higher APY on the same balance is the most direct boost. Even half a percent, compounded over decades, is meaningful.
• Compound more often. Switching from annual to monthly compounding helps a little; monthly to daily helps only marginally. Treat frequency as a tie-breaker, not a strategy.
• Reinvest, don't withdraw. The whole engine depends on leaving interest in the account so it can earn more interest. Pulling earnings out converts compound growth back into something closer to simple interest.

Compounding frequency, in real dollars

It helps to see how much frequency actually moves the needle. Take a $10,000 deposit at a 5% nominal rate left for 10 years, and change only how often it compounds:

• Annually (m = 1): the balance grows to about $16,289, for roughly $6,289 in interest.
• Quarterly (m = 4): about $16,436, or roughly $6,436 in interest.
• Monthly (m = 12): about $16,470, or roughly $6,470 in interest.
• Daily (m = 365): about $16,487, or roughly $6,487 in interest.

The jump from annual to monthly is worth about $181 over the decade; the further jump from monthly all the way to daily adds only about $17. That pattern - a noticeable gain when you first add compounding periods, then rapidly shrinking returns - is why frequency is a useful tie-breaker between two otherwise identical accounts but never the headline reason to pick one. The same $10,000 at 5% under simple interest would earn a flat $5,000, so every compounding option above beats it; the question is only by how much. Plug your own numbers into the fields to watch the gap between simple and compound widen with the rate and the time horizon.

Where simple and compound interest show up in real products

Knowing which method a real account or loan uses is what makes this calculator practical rather than just a math exercise. A few common cases:

• Savings accounts and CDs almost always use compound interest, usually compounded daily and credited monthly. Banks advertise the result as APY, so the rate you see already reflects compounding. To project a CD's payout at maturity, use the compound side here or the dedicated Compound Interest Calculator.
• Bonds typically pay simple interest in the form of fixed coupon payments on the face value, though zero-coupon bonds behave more like a compounding lump sum because the discount accretes over time.
• Many auto loans and personal loans are quoted as simple-interest loans, but because you make regular payments that pay down the balance, the interest you actually pay follows an amortization schedule rather than the single-lump simple formula.
• Credit cards compound aggressively - typically daily on the average balance - which is why a carried balance grows so fast. The compound side of this tool mirrors exactly what unpaid debt does to you, just in reverse.
• Student loans often accrue simple daily interest, but unpaid interest can be capitalized (added to the principal) at certain points, at which moment it effectively starts compounding.

When in doubt, read the account disclosure or loan agreement for the words "compounded" and the frequency, or simply compare the quoted APY against the nominal rate - if they differ, compounding is in play.

Limitations and assumptions

This calculator is a planning estimate, not a guaranteed return. Keep these assumptions in mind:

• It assumes a fixed rate for the whole period. Real savings rates and investment returns vary year to year.
• It grows a single lump sum with no additional deposits or withdrawals. Regular contributions would raise the final balance.
• It shows gross interest. Interest income is generally taxable, so your after-tax return is lower.
• It does not adjust for inflation, which erodes the purchasing power of the final balance over long periods.
• It ignores account fees and early-withdrawal penalties that some products charge.

How it compares to related calculators

This page answers "simple vs compound on a lump sum." If your question is different, a sister tool fits better:

• For compound growth only, with a cleaner breakdown, use the Compound Interest Calculator.
• For simple interest on a loan or note, use the Simple Interest Calculator.
• To plan regular monthly deposits toward a goal, use the Savings Calculator, or set a target amount and date with the Savings Goal Calculator.
• To solve for the rate you need given a target balance, use the Interest Rate Calculator.

Sources

• Consumer Financial Protection Bureau (CFPB) - What is compound interest?
• Consumer Financial Protection Bureau (CFPB) - Interest rate vs. APR.
• U.S. Securities and Exchange Commission (Investor.gov) - Compound interest and the math of investing.
• Federal Deposit Insurance Corporation (FDIC) - Consumer resources on deposit accounts and APY.