[60] Barry wants to set up an annuity that will pay him $3,000 per month for 20 years beginning when he turns 65 years of age. If his current age is 50 years and the invested funds will earn 6.5% compounded monthly, what amount must he invest today?
[61] Samuel recently inherited money from his grandfather’s estate. He wants to purchase an annuity that will pay $5,000 every 3 months between age 60 (when he plans to retire) and age 65 (when his permanent pension will begin). The first withdrawal is to be 3 months after he reaches 60, and the last is to be on his 65th birthday. If Sam is currently 50.5 years old, and the invested funds will earn 6% compounded quarterly, what amount must he invest today?
[62] It is time to start saving for your retirement. You are 40 years old and want to retire when you turn 60. You will deposit $1,000 into an RRSP at the beginning of every month for 20 years. You will then use the accumulated funds to purchase a 15-year annuity with the first withdrawal one month after your 60th birthday. Assume that the RRSP earns 7% compounded monthly, and the funds invested in the annuity earn 5% compounded monthly.
a. Find the size of the monthly withdrawals.
b. You decide that you will need at least $5,000 per month to live on when you retire at age 60. How much extra money must you contribute to your RRSP each month so you can withdraw $5,000 every month for 15 years?
[63] Starting today, Giselle Lafleur will deposit $200 in her RRSP each month for 20 years. One month after the last deposit, she will withdraw the money in equal monthly withdrawals for 10 years.
a. Find the size of the monthly withdrawals if the invested funds earn j12 = 9%.
b. How much interest will Miss Lafleur earn over the next 30 years?
[64] You have just celebrated your 20th birthday. You want to retire when you turn 65. Starting today, you are going to make monthly contributions to your RRSP, so that when you retire, you can withdraw $2,250 per month for 15 years. The first withdrawal is made when you turn 65. You anticipate the invested funds will earn 7% compounded monthly.
a. How much money must you contribute each month to your RRSP to achieve your goal?
b. How much interest did you earn during the entire time?
[65] Jean is thinking about retiring in five years. He would like to have $50,000 in an account when he retires. He decides to make monthly deposits (at the beginning of each month) in his local credit union, where he can earn 7.0% compounded quarterly.
a. What would be the required monthly deposit to accumulate $50,000 in five years?
b. How much interest does John earn over the 5 years?
[66] Six years from now, when you turn 55, you are planning to retire. You want to set aside some money today so you can receive $2,500 at the end of every quarter for 15 years, with the first withdrawal 3 months after you turn 55. The invested funds earn 9% compounded semiannually.
a. What amount must you invest today?
b. How much interest will you earn during the 21 years?
Perpetuities and General Annuities
[67] You have become wealthy beyond your wildest dreams and would like to create a scholarship at BCIT. You would like to give $2,000 per year to a student studying business math. You would like your scholarship to continue in perpetuity.
a. How much money should you set aside today if the first payment is in one year and the interest rate is 8% compounded annually?
b. How much should you set aside if the first scholarship is today?
[68] You take out a loan to buy a black Honda S2000 convertible sports car with leather interior. The bank requires that you put $9,000 down, followed by payments of $925 at the end of every month for 5 years.
a. If the bank charges you 12% interest compounded monthly, what is the selling price of your car?
b. If the bank charges you 12% interest compounded semiannually, how much would your monthly payments be? Note: You borrow the same amount as found in part (a).
[69] Mr. Bean borrows $7,500 today. He will repay the loan with quarterly payments at the end of every three months for three years. The interest rate charged is 9% compounded monthly. Find the size of the payment.
[70] A corporation donates $11,000 to Langara. The funds are invested at 10% compounded annually per year. The interest is paid out each year as a scholarship. How much will be paid out each year if the first scholarship is paid immediately after the donation is received? Note: It’s easier to use the calculator.
[71] You have just won the Set for Eternity Lottery; the lottery will pay you and your descendants $5,000 per month forever, with the first payment in one month. Instead of receiving $5,000 per month forever, you would like to receive the cash now. What is the cash value of the prize if the interest rate is j12 = 6%?
[72] The TRIUMF research lab at UBC recently received a donation from a private individual. The funds were matched two-to-one by the government. Each year, they plan to pay out a scholarship of $8,596.59 as they anticipate earning 11% compounded quarterly on the invested funds. What amount did the private individual donate? (The first scholarship will be one year later.) Round answer to the nearest dollar.
[73] You have decided to purchase preferred shares of Plutonium Fuel Cells Inc. that pay a semiannual dividend of $1.25 per share.
a. What would you be willing to pay per share if you want to earn at least 5% compounded semiannually on your investment, and the next dividend is to be paid in 6 months?
b. You are short of cash and need to sell your shares of Plutonium Fuel Cells Inc. Unfortunately, interest rates have risen to 8% compounded semiannually. Calculate your gain or loss per share if the next dividend is due in six months, and the dividend per share remains the same.
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