Question

The PRESENT VALUE of $2,000 would be smaller if interest were compounded quarterly rather than annually

True or False

Answer 1

True

To understand this we need to understand the concept of effective interest.

For example if an amount is compounded once a year at 6% then the effective rate of interest would be 6% as it is only compounded once in a single year. (1000 will become 1060 at 6%)

If an amount lets take an example 1000 is compounded after 6 months and interest is 6% then the amount would be compounded accordingly:

After 6 months it will be compouned at 6/2% = 3% so 1000 will become 1000 + 1000 * 0.03 = 1030

Now at the end of one year, 1030 will again compounded at 3% so 1030 will become 1030 + 30.9 = 1060.9

The more it is compounded the effective rate would be higher thus if an amount is discounted compounding quarterly in comparison to compounded yearly then the value of $2000 would be smaller.