Compound Interest Calculator: Future Value, Savings, Loan Repayments, Effective Rate and Doubling Time
Compound interest, savings and loan maths, with the working.
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How this calculator works
Choose compound interest, simple interest, regular savings or a loan.
Enter the amount, the yearly rate, the years and how many times a year interest or payments happen.
For savings enter the deposit each period. For a loan enter how many payments have been made to see the balance owing.
Formulas used
- A = P\left(1 + \frac{r}{m}\right)^{mt}
- A = Pe^{rt}
- FV = PMT\,\frac{(1 + i)^n - 1}{i}
- PMT = \frac{Pi}{1 - (1 + i)^{-n}}
Worked example
With the default numbers in the calculator above:
- Future value: 16470.09
- Interest earned: 6470.09
- Effective annual rate (the yearly rate with the compounding included): 5.12 %
- Time to double: 13.89 years (the rule of 72 gives 14.40)
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? Regular savings (a deposit each period); Amount: the lump sum, the starting balance or the loan 0.
- Interest rate each period and number of periods: 0.0041667 per period, 120.00 periods
- Growth of the starting balance: 0.00
- Growth of the regular deposits (deposits at the end of each period): 77641.14
- Total future value: 77641.14
- Total you put in, and the interest earned: 60000.00 put in; 17641.14 interest
Common questions
What is the compound interest formula?
A = P (1 + r/m) to the power mt, where P is the amount, r the yearly rate as a decimal, m the periods per year and t the years.
What is the difference between simple and compound interest?
Simple interest is paid only on the original amount. Compound interest is also paid on the interest already added.
How is a loan repayment worked out?
The repayment is the amount that makes the loan zero after all the payments, with interest on the balance each period.
How long to double my money?
About 72 divided by the percent rate, or exactly ln 2 over ln of one plus the effective rate.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any school or first-year mathematics text (financial mathematics). General information only, not financial advice.
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