Question

Would you rather have a savings account that pays 6% interest compounded semi-annually or one that pays 6% compounded monthly? Why?

Answer 1

Example-1 interest compounded semi-annually

Let take $100 invested at 6% interest compounded semi-annually for 3 years

Future value = $100 * [1 +(0.06 / 2)]^{3 * 2}

Future value = $100 * (1.03)⁶ = $119.4052

Example-2 interest compounded monthly.

Let take $100 invested at 6% interest compounded Monthly for 3 years

Future value = $100 * [1 + (0.06 / 12]^{12 * 3}

Future value = $100 * [1.005]³⁶

Future value = $119.67

So, the future value in case if interest compounded monthly will be greater than the interest compounded semi-annually because interest is compounded more number of times in case of monthly compounding which results in increase of future value due to increase in interest on interest portion.