1. How much must an organization invest in a mutual fund today in order to sell its shares for $50,000 in three years, assuming the average annual market return will be 9%, compounded biweekly (i.e., every two weeks)?

2. An organization plans to save $10,000 per month for a new building. The organization also will invest $15,000 it already has in reserves. (Hint: When a problem involves monthly payments, assume monthly compounding.)

a) What annual rate of return must the organization earn in order to accumulate $800,000 at the end of five years?

b) If the organization can only earn an annual rate of 6%, how many years will it need to accumulate $800,000?

3. A small, private college is starting a scholarship fund. The college’s fund managers expect the investments in the fund will earn an average annual return of 8%.

a) If the college deposits $10,000 into the scholarship fund on the first day of each month, how much money will be in the fund in 20 years?

b) After those 20 years have passed, how much in scholarship money can the college pay out on the first of each month for the next 25 years? (Assume the college will cease deposits into the fund.)

4. Ten years ago, an organization took out a $350,000 30-year mortgage with a 4.75% annual interest rate. Now, it is taking advantage of low interest rates to refinance the mortgage. The organization will pay $7,600 in up-front fees for a new 30-year mortgage with a 2.5% annual interest rate. The organization can earn an annual return of 2% on any money it saves.

a) The new mortgage will be $300,000—enough to pay off the old mortgage and buy some new furniture. Ignoring the up-front fees for now, how much will the organization save each month by refinancing? (Hint: Mortgage payments are monthly cash outflows.)

b) How many years will it take the organization to recover the up-front fees? (Hint: Treat the savings as a monthly cash inflow.)

c) How much money will the organization save in total (in today’s dollars) over the next 20 years?