Question

When comparing two investments with the same nominal rate, one with a 4-year term and semi-annual compounding and one with a 2-year term and quarterly compounding, the effective rate of the 4-year term instrument is ____ the effective rate of the 2-year term instrument.

Answer 1

Let say,

Nominal Rate = 12%

We know that,

(1+ Effective Rate) = (1+ periodic rate)^number of periods

4 year term with semi annual compounding:

Semi annual rate = 6%

number of period = 8

Effective Rate = (1+0.06)^8 - 1 = 59.38% Answer

2 year term with quarterly compounding:

Quarterly Rate = 3%

number of period = 8

Effective Rate = (1+0.03)^8 - 1 = 26.68% Answer

The effective rate of the 4-year term instrument is higher than the effective rate of the 2-year term instrument.