Calculate how your investments grow over time with compound interest. See the power of compounding and plan your financial future.
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. This creates exponential growth over time.
Starting with $1,000 at 5% annual interest, you earn interest on interest!
Given: You deposit $5,000 in a savings account earning 4% annual interest, compounded monthly, for 3 years.
Solution:
P = $5,000, r = 0.04, n = 12, t = 3
A = 5000 × (1 + 0.04/12)12×3
A = 5000 × (1.00333)36
A = 5000 × 1.1273 = $5,636.45
Interest earned: $636.45
Given: Invest $10,000 at 7% annual interest, compounded quarterly, for 20 years.
Solution:
P = $10,000, r = 0.07, n = 4, t = 20
A = 10000 × (1 + 0.07/4)4×20
A = 10000 × (1.0175)80
A = 10000 × 4.0246 = $40,246.37
Interest earned: $30,246.37
Given: Starting at age 25, you invest $200/month at 8% annual interest, compounded monthly, until age 65.
Solution: Using future value of annuity formula:
Monthly contribution = $200, r = 0.08, n = 12, t = 40
FV = 200 × [(1 + 0.08/12)480 - 1] / (0.08/12)
FV = 200 × [25.39 - 1] / 0.00667
FV = $702,856.25
Total contributions: $96,000 | Interest earned: $606,856.25
Given: $2,500 invested at 5% annual interest, compounded daily, for 5 years.
Solution:
P = $2,500, r = 0.05, n = 365, t = 5
A = 2500 × (1 + 0.05/365)365×5
A = 2500 × (1.000137)1825
A = 2500 × 1.2840 = $3,210.06
Interest earned: $710.06
Given: $10,000 at 6% for 10 years - compare annual vs. daily compounding.
Annual: A = 10000 × (1.06)10 = $17,908.48
Daily: A = 10000 × (1 + 0.06/365)3650 = $18,220.29
Difference: $311.81 more with daily compounding
Higher compounding frequency = slightly more interest earned
Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. Often described as "interest on interest," it makes your money grow faster than simple interest.
Albert Einstein reportedly called compound interest the "eighth wonder of the world." The longer you let your money compound, the more dramatic the growth becomes:
Simple interest is calculated only on the principal amount. Compound interest includes interest on previously earned interest, resulting in exponential growth rather than linear growth.