Exam 10: Annuities: Future Value and Present Value

Jason is considering one of two options. The first option is to receive $500 per month for the first 3 years and $850 per month for the last 2 years based on an interest rate of 3.3% compounded semi-annually. The second option is to receive $35,000 now. Determine which option should be chosen to maximize benefits now.

Determine the future value (accurate to the cent) of the ordinary general annuity:

A 20-year mortgage requires payments of $1,409.88 per month at an interest rate of 5.8% compounded monthly? What was the amount of the mortgage? What is the outstanding balance of the mortgage after 12 years?

Fred and Ethel are going to take out a business loan on which they will make annual payments of $7,500 for six years. At that point in time they will also pay off the remaining balance which will be $37,155. Their interest rate is 7.6% compounded semi-annually. What is the amount that Fred and Ethel borrowed?

The winner of a "Fifty-million dollar" lottery prize is actually entitled to payments of $500,000 at the end of every six months for 50 years. The winner can select to receive a single lump sum payment equal to the present value of these payments calculated using a rate of 9.8% compounded semi-annually. What would be the amount of the single payment?

A mortgage broker offers to sell you a mortgage loan contract that will pay $800 at the end of each month for the next 3½ years, at which time the principal balance of $45,572 is due and payable. What is the highest price you should pay for the contract if you require a return of at least 7.5% compounded monthly?

What is the cash price of a dining set if monthly payments of $200 are made for three years at an interest rate of 8.5% compounded monthly?

George is planning to have a retirement income of $7,000 at the end of every three months for the first 15 years that he is retired and then increase it to $10,000 every three months for the next 10 years. If his retirement funds earn 9.0% compounded quarterly, how much money must he have when he retires?

How much more will you have in your RRSP at age 65 if you begin annual $1,000 contributions to your plan on your 26^th birthday instead of on your 27^th birthday? Assume that the RRSP earns 8% compounded annually and that the last contribution is on your 65^th birthday.

Rajeev's new financial plan calls for end-of-quarter contributions of $2,000 to his RRSP. In addition, at each year-end, he intends to contribute another $5,000 out of the annual bonus he receives from his employer. What will be the amount in his RRSP after four years if it earns 7% compounded quarterly?

At the end of every six months for the last six years Vincent has borrowed $1,000 from Charley at an interest rate of 11% compounded semi-annually. He has not made any payments to reduce his debt. How much, including interest, does Vincent owe Charley now?

The owner of a certain investment is entitled to receive $38 at the end of every six months for 11 years plus an additional single payment of $1,000 in 11 years. Mandy is thinking about purchasing this investment. If Mandy requires a rate of return of 8.4% compounded semi-annually what is the value of this investment to her?

Franco purchased heavy machinery costing $95,000. The terms of the purchase were for monthly payments over 6 years at an interest rate of 6.5% compounded monthly. At the end of the 4^th year, Franco wanted to trade in this machinery for a newer model. Determine the balance owing on the old machinery at the end of year 4.

Max invested $9,000 per year in his RRSP each year for 20 years. If interest is 4% compounded quarterly, determine how much interest was earned at the end of this period.

How much larger will the value of an RRSP be at the end of 25 years if the contributor makes month-end contributions of $300 instead of year-end contributions of $3600? In both cases the RRSP earns 6.5% compounded semi-annually.

Jeannette plans to contribute $4,000 per year for the first 5 years; $5,000 per year for years 6 - 10; $6,000 per year for years 11 - 15; and $7,000 per year for years 16 - 20. If the rate of return on her investment is 3.5% compounded annually, determine the future value at the end of year 20.

Determine the future value:

A victim of a car accident won a judgment for wages lost over a two-year period ended nine months before the date of the judgment. In addition, the court awarded interest at 6% compounded monthly on the lost wages from the date they would have otherwise been received to the date of the judgment. If the monthly salary was been $5,500, what was the total amount of the award (on the date of the judgment)?

How much money could be borrowed at 7% compounded semi-annually if the borrower can make monthly payments of $875 for 25 years?

Gloria has just made her ninth annual $2,000 contribution to her Tax-Free Savings Account (TFSA). She now plans to make semi-annual contributions of $2,000. The first contribution will be made six months from now. How much will she have in her TFSA 15 years from now if the plan has earned and will continue to earn 5% compounded quarterly?