Get the most from your savings and investments with our free Compound Interest Calculator. Knowing that money grows over time with compounding interest is the key to managing your finances and being well-informed to make future financial decisions.
What is Compound Interest?
Compound interest is the interest earned on both the principal amount and the interest that accumulates over time. It motivates the savings to grow faster.
Compound Interest Formula
The formula to calculate compound interest is:
A = P × (1 + r/n)^(n × t)
Where:
- A = Final amount (principal + interest)
- P = Principal amount (initial deposit or investment)
- r = Annual interest rate (in decimal form, e.g., 5% = 0.05)
- n = Number of compounding periods per year
- t = Time in years
Compound Interest (CI) = A - P
Example Without Contributions
Scenario: You invest 10,000 with an annual interest rate of 6% compounded monthly for 5 years.
Using the formula:
- P = 10,000
- r = 0.06
- n = 12 (monthly compounding)
- t = 5 years
A = 10,000 × (1 + 0.06/12)^(12 × 5)
A = 10,000 × (1 + 0.005)^(60)
A ≈ 10,000 × 1.34885
A ≈ 13,488.50
Compound Interest = A - P = 13,488.50 - 10,000 = 3,488.50
So, the total amount after 5 years will be 13,488.50, and the interest earned is 3,488.50.
Example With Monthly Contributions
Scenario: You start with 5,000 and contribute 500 each month for 3 years at an annual interest rate of 4%, compounded monthly.
To calculate this, we use the future value of a series formula:
A = P × (1 + r/n)^(n × t) + (C × [(1 + r/n)^(n × t) - 1] / (r/n))
Where:
- P = 5,000 (initial amount)
- C = 500 (monthly contribution)
- r = 0.04
- n = 12 (monthly compounding)
- t = 3 years
Step 1: Calculate the growth of the initial investment:
A_initial = 5,000 × (1 + 0.04/12)^(12 × 3)
A_initial ≈ 5,000 × 1.12749 ≈ 5,637.45
Step 2: Calculate the growth of monthly contributions:
A_contributions = 500 × [(1 + 0.04/12)^(12 × 3) - 1] / (0.04/12)
A_contributions ≈ 500 × [1.12749 - 1] / 0.003333
A_contributions ≈ 500 × 38.247 ≈ 19,123.50
Total Amount = A_initial + A_contributions ≈ 5,637.45 + 19,123.50 = 24,760.95
.jpg)
.jpg)