Question

You are given the opportunity to put your money in one of two savings account. Account 1 compounds interest monthly at a rate of 0.4%. Account 2 compounds every year at a rate of 4.8%. Which account would you choose and why?

Answer 1

Choose Account 1 with monthly compounding at 0.4% for its slightly higher effective annual rate (EAR) of approximately 4.88%, compared to Account 2's 4.8% with annual compounding. The frequent compounding in Account 1 offers a better return on investment due to the nature of compound interest.

Step-by-step explanation:

If you are deciding whether to put your money into Account 1, with monthly compounding at a rate of 0.4%, or into Account 2, with annual compounding at a rate of 4.8%, you should compare the effective annual rates (EAR) of both accounts to make an informed decision. The effective annual rate takes into account the frequency of compounding and gives you the true annual rate.

For Account 1, with monthly compounding, the EAR can be calculated with the formula (1 + monthly interest rate)12 - 1. Therefore, EAR for Account 1 is (1 + 0.004)12 - 1, which equates to an EAR of approximately 4.88%.

Account 2, on the other hand, compounds annually at a rate of 4.8%, which means its EAR is also 4.8%. Comparing the two EARs, we can see that Account 1 offers a slightly higher return on investment due to the monthly compounding effect. The power of compound interest lies in the frequency with which it is compounded; the more frequent the compounding, the higher the accumulated interest.

Therefore, Account 1 would be my choice due to its higher effective annual rate, which is a result of monthly compounding as opposed to annual compounding in Account 2.