Simple vs Compound Interest
Hesaplayıcı2 min read
Short answer
With simple interest, interest applies to the principal only; with compound interest, each period's interest joins the balance and earns interest too. At the same principal and rate, the gap grows with the term. For example, 100,000 TRY at 40% a year becomes 300,000 TRY in 5 years with simple interest and 537,824 TRY compounded yearly.
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 (0.40 for 40%)
- t: term in years
- n: compounding periods per year: yearly 1, monthly 12
With simple interest the balance grows by the same amount every year; with compound interest it grows by the same rate.
Step-by-step example
100,000 TRY at 40% a year for 2 years; the compound case compounds yearly:
- Simple interest, year 1: 100,000 × 0.40 = 40,000 TRY interest; balance 140,000 TRY.
- Simple interest, year 2: the interest is again 40,000 TRY on the principal; final amount 180,000 TRY.
- Compound interest, year 1: 40,000 TRY interest; balance 140,000 TRY.
- Compound interest, year 2: the interest is on 140,000 TRY; final amount 140,000 × 1.40 = 196,000 TRY.
- Difference: 196,000 − 180,000 = 16,000 TRY. That is the interest the first year’s 40,000 TRY earned in the second year.
Comparison by term
100,000 TRY at 40% a year, three methods:
| Term | Simple interest | Compound, yearly | Compound, monthly |
|---|---|---|---|
| 6 months | 120,000.00 TRY | 118,321.60 TRY | 121,742.62 TRY |
| 1 year | 140,000.00 TRY | 140,000.00 TRY | 148,212.65 TRY |
| 2 years | 180,000.00 TRY | 196,000.00 TRY | 219,669.89 TRY |
| 3 years | 220,000.00 TRY | 274,400.00 TRY | 325,578.57 TRY |
| 5 years | 300,000.00 TRY | 537,824.00 TRY | 715,198.09 TRY |
| 10 years | 500,000.00 TRY | 2,892,546.55 TRY | 5,115,083.10 TRY |
With monthly compounding the effective annual rate is 48.21%. In ten years, simple interest multiplies the principal by 5 and yearly compounding by about 29.
Terms shorter than one period
If the term is shorter than one compounding period, compound interest does not beat simple interest. For the 6-month term in the table, yearly compounding with a fractional exponent gives 118,321.60 TRY; simple interest gives 120,000 TRY. At exactly one year the two are equal, and from the second year compound interest pulls ahead.
Where each one is used
Turkish banks calculate the interest of a single term on a TRY time deposit with simple interest. When the deposit is renewed and the interest is added to the principal, the savings grow with compounding. The inflation and investment return calculators also use compounding. When you compare offers, compare the effective annual rate, not the nominal rate.
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%