If we invest money for 10 years at 8% interest, compounded semi-annually, we are really investing money for ______ six month periods, during which we receive _______ percent interest each year.

To get the answer to this question, we need to break it down into several steps.

Step 1: Find the number of compounding periods
The investment is compounded semi-annually, meaning interest is added twice a year. Since we are investing for 10 years, we need to find the number of six-month periods in 10 years. To do this, we multiply the number of years (10) by the number of six-month periods in a year (2):
10 years * 2 six-month periods = 20 six-month periods

Step 2: Find the interest rate per period
The yearly interest rate is 8%. Since interest is added semi-annually, we need to find the interest rate for each six-month period. To do this, we divide the yearly interest rate (8%) by the number of compounding periods in a year (2):
8% / 2 = 4% interest per six-month period

Therefore, we are really investing money for 20 six-month periods, during which we receive 4% interest each year.

To determine the number of six-month periods in 10 years, we need to multiply 10 by 2 since there are 2 six-month periods in a year.

10 years * 2 six-month periods/year = 20 six-month periods

Next, to determine the interest rate for each six-month period, we divide 8% by 2 since the interest is compounded semi-annually.

8% / 2 = 4% interest for each six-month period

Therefore, we are really investing money for 20 six-month periods, during which we receive 4% interest each year.