Answer to Question #65536 in Financial Math for Rammeya

Question

Find the nominal annual rate of interest compounded semi-annually that is equivalent to 4.2 %4.2% compounded quarterly. round 4 decimals

Answer 1

Find the nominal annual rate of interest compounded semi-annually that is equivalent to 4.2% compounded quarterly.
Effective rate of​ interest can be calculated using formula: r = (1 + i/n)^n - 1, where i - nominal interest rate, n - number of compounding periods.
r = (1 + 0.042/4)^4 - 1 = 0.0427 or 4.27%.
If interest is compounded semi-annually, then nominal rate of interest that maintain the same effective rate of​ interest is:
(1 + i/2)^2 - 1 = 0.0427,
(1 + i/2)^2 = 1.0427,
1 + i/2 = 1.0211,
i/2 = 0.0211
i = 0.0422 or 4.22%.