You have $500 that you would like to invest. You have 2 choices: Savings Account A which earns 8% compounded annually or Savings Account B which earns 7.75% compounded semiannually. Which would you choose and why

Savings account A is more profitable because it provides a higher real interest rate.

Explanation:

Giving the following information:

Savings Account A:

Nominal interest rate= 0.08

Savings Account B:

Nominal interest rate= 0.0775/2= 0.03875

Investment= $500

The most profitable savings account is the one with a higher real annual interest rate.

Real interest rate= [(1+i)^n] - 1

Savings account A:

Real interest rate= (1.08^1) - 1= 0.08

Savings account B:

Real interest rate= (1.03875^2) - 1= 0.079

Savings account A is more profitable.

Prove:

Savings account A:

FV= 500*(1.08^1)= $540

Savings account B:

FV= 500*(1.03875^2)= $539.5

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