Merchants Bank offers to lend you $30,000 at a nominal rate of 6.0%, simple interest, with interest paid quarterly. Gold Coast Bank offers to lend you the $30,000, but it will charge 7.0%, simple interest, with interest paid at the end of the year. What's the DIFFERENCE in the effective annual rates charged by the two banks?

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) for Merchants Bank is calculated using the formula for simple interest with quarterly payments: EAR = (1 + (0.06/4))^4 - 1 = 6.136%. For Gold Coast Bank, the EAR is simply the nominal rate since interest is paid annually: 7.0%. The difference is 7.0% - 6.136% = 0.864%, which rounds to 0.86%.

Merchants Bank Offers to Lend You $30,000 at a Nominal