1. Petros wishes to retire in 10 years from NOW. He has $250,000 in his RRSP currently and will contribute $5000 at the beginning of each month. If the RRSP earns 5% compounded semi-annually, how much will he have at retirement?
2. Rocky currently has $85,000 in his RRSP. He is going to contribute $5000 at the end of every six months for the next 18.5 years and then use the funds to purchase an annuity for 15 years that will pay him at the end of each month. If the RRSP gets 6.50% compounded semi-annually and the annuity gets 4.0% compounded monthly, what size payment will he get?
3. With end of month contributions of $251.33, an investment account is expected reach $100,000 in value after 15 years and 5 months.
(a) Determine the nominal rate of return to reach this projected growth.
(b) Determine the effective rate of return to reach this projected growth.
4. Cat has $300000 in her RRSP. She will contribute for another 10 years and then let the plan grow for an additional 7 years. The RRSP earns 5.5% compounded annually. How much should she contribute at the end of every six months in order to have $1,000,000 in her RRSP 17 years from now?
5. What will be the amount in an RRSP after 25 years of contributions of $800 at the beginning of each year for the first 10 years and $1300 yearly for the remaining years? Assume the RRSP will earn 6% quarterly.
6. What quarterly compounded nominal rate and effective rate of interest are being charged on a $5000 loan if quarterly payments of $302.07 will repay the loan in 5.5 years?
(a) The nominal rate is:
(b) The effective rate is:
7. Brad Pitt gave one of his dozen kids $200,000 when she was born. He told Pita that she had to leave the money invested until she was 21 and then she could get end of month payments for 10 years. Assume that the entire investment earned 8.75% compounded monthly, how much were Pita Pitt's monthly cheques?
8. Charlie's Angels Appliance Centre is advertising refrigerators for six monthly payments of $159 including a payment on the date of purchase. What cash price will he accept if the prevailing interest rate is 17% compounded monthly?
9. The MSRP on a new Bose stereo system is $38875. The interest rate on a 48-month lease is 1.9% compounded monthly. What is the monthly lease payment assuming a down payment of $5450 and a residual value of $12000?
10. A deferred annuity is comprised of 8 annual payments of $1500. What is the period of deferral if the present value of the payments, discounted at 7.9% compounded annually is $6383.65?
11. The Fine brothers (Curly, Larry & Moe) signed a 7 year lease on a new dump truck for their new construction business. They want to report the lease as a long term liability. The lease payments of $1500 are made at the beginning of each month and the interest on the lease is set at 9% compounded monthly.
(a) What initial liability can the boys report on their balance sheet?
(b) How much of the liability will be reduced during the second year of the lease?
12. What duration of annuity paying $8500 at the end of every quarter can be purchased with $300,000 in the invested funds earn 4.5% compounded semi-annually?
State your answer as an integer representing the number of quarterly periods.
13. Dolly has just opened a Registered Education Fund for her daughter Lolly. She wants to contribute $3000 at the beginning of each half year for four years starting nine years from now when Lolly enters College. What semi-annual contributions, including one today must they make for the next nine years in the RESP earns 8.25% compounded semi-annually?
14. What amount is required to fund a perpetuity that pays $8500 at the beginning of each quarter? The funds can be invested to earn 5.0% compounded quarterly.
15. Simon donated $750,000 to the Junior Idol Hopefuls to fund a perpetuity of five annual bursaries for students of the singing school. If the first of the five bursaries are to be awarded immediately, what is the maximum amount of each bursary? Assume the fund earns 4.2% compounded semi-annually.
16. A Pet Cemetary sells plots for $3000 plus an amount calculated to provide for the cost of maintaining the grounds in perpetuity. This cost is $55/month due at the end of each month. If the funds are invested at 8.5% compounded quarterly, what is the price of a plot?