Interest Calculators

0 calculators tagged with “Interest”

Interest is the cost of borrowing money or the return earned on invested money, expressed as a percentage of the principal over a time period. Simple interest is calculated only on the principal: I = P × r × t. Compound interest is calculated on the principal plus accumulated interest, growing exponentially: A = P(1 + r/n)^(nt). The effective annual yield (EAY or APY) reflects the true annual return accounting for compounding frequency. Understanding interest calculations is fundamental for loans, savings, investments, mortgages, and credit cards.

All Calculators

No calculators found for this topic.

Simple Interest

I = P × r × t

P = principal; r = annual interest rate (decimal); t = time in years. A = P + I = P(1 + rt).

Example: $5,000 at 6% for 3 years: I = 5,000 × 0.06 × 3 = $900. A = $5,900.

Compound Interest

A = P × (1 + r/n)^(nt)

n = compounding periods per year (1 = annual; 12 = monthly; 365 = daily). Continuous: A = Pe^(rt).

Example: $5,000 at 6% compounded monthly for 3 years: A = 5,000 × (1 + 0.06/12)^(12×3) = 5,000 × (1.005)^36 = 5,000 × 1.1967 = $5,983.40.

APR vs. APY

APR (Annual Percentage Rate): nominal rate, does not account for compounding. APY (Annual Percentage Yield) or EAY: effective rate including compounding: APY = (1 + APR/n)^n − 1. Example: 6% APR compounded monthly: APY = (1 + 0.005)^12 − 1 = 1.0617 − 1 = 6.17%.

Credit Card Interest

Daily periodic rate = APR / 365. Interest = average daily balance × daily rate × days in billing cycle. Example: $2,000 balance, 24% APR: daily rate = 0.24/365 = 0.000657. Monthly interest ≈ 2,000 × 0.000657 × 30 = $39.40.

Glossary

Compound Interest
A = P(1+r/n)^(nt); interest calculated on principal plus accumulated interest; grows exponentially; n = compounding periods per year; continuous compounding: A = Pe^(rt).
APY (Annual Percentage Yield)
The effective annual rate accounting for compounding: APY = (1+APR/n)^n − 1; higher than APR when n > 1; must be disclosed for US savings accounts; represents the true annual return.
Simple Interest
I = P × r × t; interest calculated only on principal; A = P(1+rt); linear growth; used for short-term loans, Treasury bills, and as a baseline comparison to compound interest.

Frequently Asked Questions

Simple interest: calculated only on the original principal. I = P × r × t. Final amount: A = P(1 + rt). Interest earned is constant each period. Example: $10,000 at 5% for 4 years: I = 10,000 × 0.05 × 4 = $2,000. Total: $12,000. Compound interest: interest earned each period is added to the principal → earns interest in the next period ('interest on interest'). A = P(1 + r/n)^(nt). Example: same $10,000 at 5% compounded annually for 4 years: A = 10,000 × (1.05)^4 = 10,000 × 1.2155 = $12,155. More compounding periods (monthly, daily) → slightly more interest.

APR (Annual Percentage Rate): the nominal annual rate without considering compounding effect. APY (Annual Percentage Yield) or EAY: the effective annual rate that accounts for compounding — the actual return or cost over one year. Conversion: APY = (1 + APR/n)^n − 1. Example: savings account offering 5% APR compounded monthly: APY = (1 + 0.05/12)^12 − 1 = 1.05116 − 1 = 5.116%. The higher the compounding frequency, the higher the APY relative to APR. For borrowers: APR on credit cards is the nominal rate — the APY (effective cost) is slightly higher. Regulatory disclosure: APY must be disclosed for savings accounts (US TISA law); APR must be disclosed for loans (US Truth in Lending Act).

A = P × (1 + r/n)^(nt). P = principal; r = annual rate (decimal); n = compounding periods per year; t = years. Common values of n: annually = 1; semiannually = 2; quarterly = 4; monthly = 12; biweekly = 26; weekly = 52; daily = 365. Example: invest $2,500 at 4.5% APR compounded quarterly for 5 years: A = 2,500 × (1 + 0.045/4)^(4×5) = 2,500 × (1.01125)^20 = 2,500 × 1.2507 = $3,126.75. Interest earned = $3,126.75 − $2,500 = $626.75. Compare to simple interest: I = 2,500 × 0.045 × 5 = $562.50. Compound interest earns $64.25 more over 5 years.

Most US credit cards use daily compounding: Daily periodic rate (DPR) = APR / 365. Average daily balance × DPR × days = monthly interest charge. Example: average daily balance $3,500; APR 22.99%: DPR = 0.2299/365 = 0.0006299/day. Monthly interest ≈ $3,500 × 0.0006299 × 30 = $66.14. Annual interest on $3,500 balance ≈ 66.14 × 12 = $793.68 ≈ 22.7% of balance. Critical point: paying only the minimum payment means most of the payment goes to interest; balance barely decreases. Full payoff of $3,500 at minimum payments (~$70/month at 23% APR): takes >7 years; total interest >$2,500. The solution: always pay more than the minimum.