For each of the following questions, draw a complete time diagram (including a timeline, time units, cash flows, interest rates, changes in interest rates, focal time, arrows, and unknown quantity):

Question 1.

Determine the lump sum of money that is needed to be invested today in order to receive $20,000 in 8 years and another $30,000 in 13 years from now if you can earn interest at

• 5%/year compounded annually for the first three years
• 6.5%/year compounded semi-annually for the next five years
• 8%/year compounded quarterly for the three years after that; and
• 10%/year compounded monthly for the following two years.

Question 2.

An annuity pays $200 at the end of each month for 2 years, then $300 at the end of each month for the next year, and then $400 at the end of each month for the next 2 years. How much does it cost to buy this annuity today if the underlying rate of return on this annuity is 10%/year compounded monthly?

Question 3.

To prepare for early retirement, a self-employed consultant makes deposits of $5,500 into her Registered Retirement Savings Plan (RRSP) each year for 20 years, starting on her 31st birthday. When she turns 51 she wishes to draw out 30 equal annual payments. What is the size of each withdrawal if interest is paid at a rate of 6%/year compounded annually until the 10th deposit and at 5%/year compounded annually for the remaining time?