The Compound Interest Calculator shows how your money grows with the power of compounding. It uses the formula A = P(1 + r/n)^(nt) to compute future value across different compounding frequencies.
Enter your principal, interest rate, and time period to see projected growth. The calculator supports four modes: future value, with regular contributions, time to reach a target, and side-by-side frequency comparison.
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The compound interest formula is: A = P * (1 + r/n)^(n * t), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the time in years.
Compound interest differs from simple interest in that interest is earned on previously accumulated interest, not just on the principal. This creates exponential growth. The more frequently interest is compounded, the higher the effective yield.
The Rule of 72 provides a quick estimate of doubling time: divide 72 by the annual interest rate to get the approximate number of years for the investment to double. At 6% interest, the principal doubles in roughly 12 years.
Problem: Invest 10,000 at 5% annual interest, compounded monthly, for 10 years.
Solution: A = 10,000 * (1 + 0.05/12)^(12 * 10) = 10,000 * (1.004167)^120 = 16,470.09.
Answer: 16,470.09 (interest earned: 6,470.09)
Problem: Invest 5,000 at 8% annual interest, compounded annually, for 20 years.
Solution: A = 5,000 * (1 + 0.08)^20 = 5,000 * 4.66096 = 23,304.79.
Answer: 23,304.79 (interest earned: 18,304.79)
Problem: Invest 20,000 at 6% for 15 years: annual vs daily compounding.
Solution: Annual: 20,000 * 1.06^15 = 47,931.64. Daily: 20,000 * (1 + 0.06/365)^(365*15) = 49,165.80.
Answer: Daily compounding yields 1,234.16 more
Problem: Starting at age 25 with 1,000, contributing nothing more, at 7% annual interest compounded annually, what is the balance at age 65?
Solution: A = 1,000 * (1.07)^40 = 1,000 * 14.974 = 14,974.
Answer: 14,974 after 40 years (the original 1,000 grew nearly 15-fold)
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