Compute the maturity amount and interest for any compounding frequency, and see exactly how much the frequency itself is worth.
| Year | Opening | Interest | Closing |
|---|
A = P (1 + r / (100 × n)) n × t
P is the principal, r the nominal annual rate as a percentage, t the time in years, and n the number of times interest is compounded per year. Compound interest is then A − P. For half-yearly compounding n = 2, so the rate per period halves and the number of periods doubles — which is why half-yearly always beats yearly at the same nominal rate.
On ₹1,00,000 at 8% for 3 years:
| Compounding | Maturity | Interest |
|---|---|---|
| Yearly | ₹1,25,971 | ₹25,971 |
| Half yearly | ₹1,26,532 | ₹26,532 |
| Quarterly | ₹1,26,824 | ₹26,824 |
| Monthly | ₹1,27,024 | ₹27,024 |
The gain from yearly to half-yearly is ₹561; going all the way to monthly adds only ₹492 more on top. Frequency matters, but with diminishing returns — the rate itself matters far more.
Amount equals principal times one plus rate divided by 200, raised to the power of two times the number of years. Halving the rate and doubling the periods is what half yearly compounding means.
Simple interest is charged only on the original principal. Compound interest is charged on the principal plus all interest added so far, so the balance grows faster and the gap widens with time.
Yes at the same nominal rate, but with diminishing returns. Moving from yearly to half yearly gains the most; beyond monthly the extra is negligible, approaching a ceiling set by continuous compounding.
The nominal rate is the quoted annual figure. The effective rate is what you actually earn once compounding is counted, so 8 percent compounded half yearly has an effective annual rate of 8.16 percent.