How to Calculate Interest
Hesaplayıcı2 min read
Short answer
Interest comes from the principal, the rate and the term. Simple interest applies to the principal only: interest = principal × annual rate × years. Compound interest adds each period's interest to the balance. For example, 50,000 TRY at 36% a year becomes 68,000 TRY in a year with simple interest and 71,288.04 TRY compounded monthly.
Formula
simple interest: A = P × (1 + r × t)
compound interest: A = P × (1 + r/n)^(n × t)
- A: final amount
- P: principal
- r: nominal annual interest rate as a decimal (0.36 for 36%)
- t: term in years
- n: compounding periods per year: yearly 1, monthly 12, weekly 52, daily 365
Total interest is A − P. With compound interest the effective annual rate is (1 + r/n)^n − 1.
Step-by-step example
50,000 TRY at 36% a year for 1 year:
- Rate and term: r = 0.36, t = 1 year.
- Simple interest: A = 50,000 × (1 + 0.36 × 1) = 68,000 TRY. The interest is 18,000 TRY.
- Monthly compound interest: A = 50,000 × (1 + 0.36/12)^(12 × 1) = 71,288.04 TRY. The interest is 21,288.04 TRY.
- Effective annual rate: (1 + 0.36/12)^12 − 1 = 42.58%.
At the same nominal rate, monthly compounding earns 3,288.04 TRY more than simple interest.
How compounding frequency changes the result
50,000 TRY at 36% a year for 1 year:
| Method | Final amount | Interest | Effective annual rate |
|---|---|---|---|
| Simple interest | 68,000.00 TRY | 18,000.00 TRY | 36.00% |
| Compound, yearly | 68,000.00 TRY | 18,000.00 TRY | 36.00% |
| Compound, monthly | 71,288.04 TRY | 21,288.04 TRY | 42.58% |
| Compound, daily | 71,653.76 TRY | 21,653.76 TRY | 43.31% |
Over exactly one year, yearly compounding gives the same result as simple interest. The gap grows with a longer term and more frequent compounding.
Monthly rates and terms in days
- If the rate is monthly, multiply it by 12: 3% a month is a nominal 36% a year. 3% a month simple interest on 50,000 TRY again gives 68,000 TRY in one year.
- If the term is in days, divide the days by 365. 50,000 TRY at 36% a year for 90 days: 54,438.36 TRY with simple interest (4,438.36 TRY interest) and 54,570.02 TRY compounded monthly.
For the withholding tax a bank takes from deposit interest, use the deposit interest calculator.
Worked example: 10,000 at 10% a year, compounded monthly, for 5 years
Final amount
16,453.09
- Total interest
- 6,453.09
- Nominal annual rate
- 10.00%
- Effective annual rate
- 10.47%
- Term
- 5 years
Step by step
Nominal annual rate
r = rate × periods per year
r = 10% × 1 = 10.00%
Term
t = years + months/12 + weeks/52 + days/365
t = 5 + 0/12 + 0/52 + 0/365 = 5 years
Final amount
A = P × (1 + r/n)^(n × t)
A = 10,000 × (1 + 10%/12)^(12 × 5) = 16,453.09
Effective annual rate
e = (1 + r/n)^n − 1
e = (1 + 10%/12)^12 − 1 = 10.47%