Answer to Question #65535 in Financial Math for Rammeya

Question

A bank pays 11.7​% compounded monthly on certain types of deposits. If interest is compounded semi-annually, what nominal rate of interest will maintain the same effective rate of​ interest?

Answer 1

A bank pays 11.7​% compounded monthly on certain types of deposits.
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 + 0.117/12)^12 - 1 = 0.1235 or 12.35%.
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 = 0.1235,
(1 + i/2)^2 = 1.1235,
(1 + i/2)^2 - 1 = 0.1235,
1 + i/2 = 1.06,
i/2 = 0.06
i = 0.12 or 12%.