Question

You have found three investment choices for a​ one-year deposit: 11.8 % APR compounded​ monthly, 11.8 % APR compounded​ annually, and 11.2 % APR compounded daily. Compute the EAR for each investment choice.​ (Assume that there are 365 days in the​ year.) ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The EAR for the first investment choice is ​%.

Answer 1

Effective annual rate(EAR) or more clearly we can say effective annual interest rate for the first investment where annual percentage rate is 11.8% and this is compounded monthly. Effective annual rate (r) = [{1 + (i/m)}^m - 1] , where i is nominal interest rate, m is compounding period over a year. In the first investment compounding period is 12. Therefore effective annual rate = [{1+(0.118/12)}^12 - 1] = {(0.127833)^12 -1} = (1.12459572 - 1) = 0.12459572 = 12.4595%.

So for the first investment effective annual rate is 12.45%.

In case of second investment annual percentage rate is 11.8% and it is compounded annually. As it is compounded annually it's effective annual rate will be also 11.8%. As effective annual rate (r) = {(1+0.118/1)^1 -1} = (1.118 -1) = 0.118 = 11.8%.

In case of third investment annual percentage rate is 11.2% and it is compounded daily i.e 365 days. In case of this annual effective rate(AER) = {(1+0.112/365)^365 - 1} = 1.118493 -1 = 0.11849364 = 11.849364%. So we can say when 11.2 annual percentage rate is compounded daily it's annual effective rate becomes 11.849364%.