Question

Bank A charges 12% compounded monthly on its business loan. Bank B charges 11.5% compounded daily. Bank C charges 11% compounded continuously. If you want to borrow money that you will return after a number of years, which bank would you choose? Justify your answer.

Answer 1

1) Bank a :

i = 12% per year or 12% / 12 = 1% per month

yearly rate = (1 +1) ^ n -1= (1 +1%) ^ 12 - 1 = (1.01) ^ 12 - 1 = 1.1268 - 1 = 0.1268 or 12.68%

2) Bank b:

i = 11.5% compounded daily

yearly rate = (1 + i / n) ^ n - 1 = (1 + 11.5% / 365) ^ 365 - 1 = (1 + 0.000315) ^ 365 - 1 = (1.000315) ^ 365 - 1 = 1.1218 - 1 = 0.1218 or 12.18%

3) Bank c:

i = 11% compounded continously

yearly rate = e ^ (i * t) - 1 = 2.7183 ^ (11% * 1) - 1 = 2.7183 * 0.11 - 1 = 1.1162 - 1 = 0.1162 or 11.62%

since the yearly rate of bank c is the lowest therefore i will choose bank c.