📖 The story
A bond pays a 6 % nominal rate, but in quarterly coupons. Investor Steve wants to know what effective rate this corresponds to through the intra-year crediting.
ℹ Four interest credits per year.
Topics › Bonds & Zero-Coupon Bonds › Quarterly coupons and the effective rate
Easy
Bonds & Zero-Coupon Bonds
Quarterly coupons and the effective rate
Change any number and press "Calculate" – or use "Type in" on the right to watch it entered.
What you learn
Quarterly interest credits bring compounding within the year – that is why the effective rate lies above the nominal rate. In comparisons the effective rate always counts.
In short: The more often interest is credited, the higher the effective rate turns out compared with the nominal rate.
Formula
i_eff = (1 + i_nom/m)^m − 1
With the example numbers
i_eff = (1 + 0,0600/4)4 − 1 = 6,14 %
How to read the formula
i_eff = (1 + i_nom/m)ᵐ − 1 shows why more frequent interest credits bring more: each intra-year credit itself earns interest again. That is why the effective rate lies above the nominal rate – and only effective rates may be compared fairly.
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