Question

A man wants to deposit $5000 into a bank account. The bank gives him two options:

Option 1: 4% interest compounded annually

Option 2: 4% interest compounded monthly (12 times each year)

Which option will earn him the most money in interest?

Answer 1

Option 2: monthly compounding

Explanation:

You want to know whether compounding 1 time per year or 12 times per year earns more interest.

Compound interest

The compound interest multiplier for compounding n times per year is ...

(1 +r/n)^n

When 4% interest is compounded 1 time per year, the effective multiplier is ...

(1 +0.04/1)^1 = 1.04

When 4% interest is compounded monthly (12 times per year), the effective multiplier is ...

(1 +0.04/12)^12 ≈ 1.04074154

Compounding 12 times per year earns more interest.

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Additional comment

On the investment of $5000, the monthly compounding will earn about $3.71 more in interest for the year.

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