Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily Explain

As a rule, assuming all else equal (rates of return, amount of investment, periods, risk, etc), the higher the compounding per year, the better. 

Let's use the given rates on this problem as an illustration. We have been given two savings account with the same nominal annual interest rate but with different compounding periods. To know which is better, we find the respective effective annual interest rates. The higher the effective rate, the higher the amount of interest that may be earned. 

Formula: Effective annual interest rate = (1 + —r — 1 

Where: r = nominal annual interest rate n = number of compounding periods 

Compute: 

5% interest compounded semiannually (twice per year): n Effective interest rate = (1 + LI —1 n 1 +0.05)2 2-1 = ( = 1.0252 — 1 = 1.050625 — 1 = 5.0625% 

5% interest compounded daily (365 times per year): Effective interest rate = (1 + LT — 1 n . (1 + 0.05 )365 — 1 365  = 1.000136986365 — 1 = 1.051267 — 1 = 5.1267%