Question

You have a goal to give back to your alma mater when you retire at age 65 (you are currently 20, so you have 45 years to go). You believe that on a yearly basis you can always earn 4%. How much do you have to save each year so that when you are 65 you can give the college $1 million? After you give the money you tell the college every year, forever they have to spend the interest on students in the engineering economic course (pay tuition, buy books, have parties, etc..). How much can be spent each year?

Answer 1

To give $1 million to your alma mater when you retire at age 65, you need to save approximately $9,009.97 each year. The college can then spend approximately $40,000 each year from the interest earned.

Step-by-step explanation:

To calculate how much you need to save each year to give $1 million to your alma mater when you retire at age 65, we can use the concept of compound interest. Assuming a constant annual return of 4%, you have 45 years to save.

Let's denote the annual savings amount as x. This amount will accumulate over the years with compound interest. So, we need to solve the equation:

$1,000,000 = x(1+0.04)^{45}$

Simplifying this equation, we find that you need to save approximately $9,009.97 each year.

After giving the college the $1 million, they can spend the interest earned each year. Since the interest rate is 4%, they can spend approximately $40,000 each year.