Compound Interest Loan Calculator (lump-sum repayment)

Understanding the compound interest loan calculator — concept and principle

Some loans are repaid in one lump sum at the end: private loans between family members, some business loans, promissory notes and deferred student debt. When no payments are made, interest is added to the balance and itself earns interest. This calculator shows the amount due at maturity, the interest, the effective annual rate and how it compares with simple interest.

How it is calculated

With principal P, annual rate r, time t in years and k compounding periods a year:

• Amount due A = P × (1 + r/k)^(k × t)
• Interest = A − P
• Effective annual rate (EAR) = (1 + r/k)^k − 1
• Simple interest = P × r × t, for comparison

Common choices for k are 1 (annual), 4 (quarterly), 12 (monthly) and 365 (daily).

The principle

Each period, interest at r ÷ k is charged on the whole balance, including interest charged before. So the balance grows by the same factor every period, which is exponential growth. More frequent compounding means interest starts earning interest sooner, so the EAR rises above the nominal rate, though with diminishing effect: as k grows without limit the amount approaches P × e^(r × t), continuous compounding. The gap between compound and simple interest widens with time and rate.

Worked example

1. Principal $10,000, 7% a year, 3 years, monthly compounding, so k = 12.
2. Periodic rate = 0.07 ÷ 12 ≈ 0.0058333, periods = 36.
3. A = 10,000 × 1.0058333³⁶ ≈ $12,329.26, so interest = $2,329.26.
4. EAR = 1.0058333¹² − 1 ≈ 7.229%.
5. Simple interest would be 10,000 × 0.07 × 3 = $2,100.00, so compounding costs $229.26 more.

For comparison, annual compounding gives $12,250.43 and daily about $12,336.53.

How to read the result

The EAR is the true yearly cost and the right figure for comparing loans that compound differently. If the amount due looks large, consider paying interest as it accrues; that keeps the cost at simple interest levels. Always check what the agreement says about compounding, since many loan contracts quote a nominal rate.

Common mistakes

• Entering the time in months when the field asks for years.
• Comparing nominal rates across loans with different compounding.
• Forgetting fees, which raise the true cost.

Frequently asked questions

How much is $10,000 at 7% compounded monthly for 3 years?

About $12,329.26, of which $2,329.26 is interest.

What is the difference between APR and EAR?

APR is usually the nominal yearly rate before compounding; EAR includes compounding within the year.

Does daily compounding make a big difference?

Compared with monthly, only a little; at 7% over 3 years it adds about $7 on $10,000.

Sources: Standard time value of money mathematics (compound interest) · CFA Institute, Quantitative Methods curriculum (effective annual rate)