These are not difficult problems. The hardest part is drawing the diagramme. Give it a try, then we can talk.
1. The LIFE LONG LOTTERY offers two possible scenarios to their winners. $250 000 cash when they trade in their ticket or $1000 at the end of each month for 25 years. If you could expect a return of 8% on your money, which option should you choose to get the best value?
a) Draw a line diagram for the monthly winnings.
b) Use the sum of a geometric series to determine the Present value of the regular payments.
2. Grant and Kera are both 75 years old. Kera is very money conscious. She was 20 years old when she began investing $1000 a year into an RRSP paying an average of 6%/a compounded annually. Grant, on the other hand, did not start to invest until age 50. He made an annual deposit of $3000 beginning at age 50. The average interest rate he received on his investment was 8%/a compounded annually.
a)What amount does each have today?
b) What should Grant have invested each year in order to have the same amount as Kera at age 75?
c) If Grant could only afford to invest $3000 per month, what average rate of interest would result in his saving the same amount as Kera?
3. Maria received $50 on her 16th birthday, and $70 on her 17th birthday, both of which she immediately invested in the bank with interest compounded annually. On her 18th birthday, she had $134.97 in her account. Draw a time line and calculate the annual interest rate.
4. Raul’s grandparents invested $1000 in a GIC for him on his 15th birthday and $2000 on his sixteenth birthday. During each of the two years the money earned 8.5% compounded annually.
a) Draw a time line to show the situation.
b) How much was in the fund on his 17th birthday?
A time line is simply a line showing the "value" of money at different times. For example, if you have $1000, what is it worth next year if you invest it at 8%?
In two years it will be worth:
You simply draw a graph with X-axis showing the years: 1,2,3,... and the Y-axis showing the value.