Compound Interest Calculator
Whats is Compound Interest ?
Compound interest is a type of interest calculation where interest is not only earned on the principal amount of a loan or investment, but also on the accumulated interest. This means that interest is calculated on both the principal amount and any interest earned in previous periods, resulting in a higher return on investment or a higher amount owed on a loan than with simple interest.
The formula for calculating compound interest is as follows:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
- P: The principal amount of the loan or investment
- r: The annual interest rate expressed as a decimal
- n: The number of times the interest is compounded per year
- t: The number of years the money is invested or borrowed
For example, if you invest $1,000 at a compound interest rate of 5% per year, compounded annually for 3 years, the total amount you would have at the end of the 3-year period would be:
P = 1000, r = 0.05, n = 1, t = 3
Compound Interest = 1,000(1 + 0.05/1)^(1x3) - 1,000
Compound Interest = $1,157.63
Final Value = $1000 + $1,157.63 = $2,157.63
As you can see, the interest earned at the end of the third year is higher than with simple interest, as interest is earned not only on the principal amount, but also on the interest earned in the previous years.
Compound interest with additional contributions
Compound interest with additional contributions is calculated using the future value of a series formula. This formula takes into account both the compounding of interest on the initial principal and the regular contributions made over time. The future value (FV) is calculated as follows:
FV = P(1 + r/n)^(nt) + PMT [ ((1+ r/n)^(nt) - 1) / (r/n) ]
Where:
- FV is the future value of the investment or loan, including interest and contributions.
- P is the principal amount (initial investment or loan amount).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the number of years the money is invested or borrowed.
- PMT is the regular contribution made at each compounding period.
Note : If contribution frequency is different than the interest compounding frequency, then the PMT mut be calculated as below.
PMT = Contribution Amount * Contribution frequency/Year ÷ Compounding Frequency/Year
Let's illustrate this with an example:
Suppose you invest $5,000 at an annual interest rate of 6%, compounded quarterly (4 times a year), and you make a monthly contribution of $100 for 5 years.
P = 5000, r = 0.06, n = 4, t = 5, PMT = 100 * 12 / 4
FV = 5000(1 + 0.06/4)^(4x5) + 100 [ ((1+ 0.06/4)^(4x5) - 1) / (0.06/4) ]
FV = 6,734.28 + 6,937.10
FV = 13,671.38
You can use this formula to calculate the future value, which represents the total amount including both the compound interest and additional contributions over the given period.
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