Exam 10: Annuities: Future Value and Present Value

If $2,000 is invested at the end of every three months, what will be the total value after 10 years? The investments earn 13% compounded annually.

Marvin has determined that he can save at least $6 per day by quitting smoking and cutting out one cup of coffee or one can of pop per day. Therefore, he has decided to make contributions of $175 to his Retirement Savings Plan (RSP) at the end of each month for 35 years. He anticipates that his RSP will earn 13.2% compounded monthly. He is 20 years old now and therefore he will be only 55 when this plan is completed. How much money will be in his RSP when he is 55 years of age?

How much more will you have in your RRSP 30 years from now if you make fixed contributions of $3,000 at the end of each of the next 30 years, instead of waiting 15 years and making annual contributions that are twice as large for half as many years? Assume that the RRSP earns 8% compounded annually.

Determine the future value of $2,800 deposited semi-annually for the first 6 years at 2.4% compounded monthly, and $550 per quarter for the remaining 4 years at 3.5% compounded annually.

Fred purchased a boat for $18,000. He paid 10% down and the balance in equal monthly payments over five years at 18% compounded monthly. What does Fred pay each month?

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

Jane is paying $506 per month for a car over five years. She had a down payment of $6,000, and is paying interest at 4.8% compounded quarterly. What was the purchase price of the car? How much interest will Jane pay overall?

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

Determine the future value in year 10 of $5,000 annual payments received in years 1, 3 and 5 and $4,000 annual payments in years 2, 4 and 6 given an interest rate of 5% compounded annually.

A mortgage broker offers to sell you a loan contract that would provide you with end-of-month payments of $900 for the next $2 \frac{3}{4}$ years. In addition, at the end of the $2 \frac{3}{4}$ year period, you will also receive a lump sum payment of $37,886. What should you pay for the contract, if you require a rate of return of 7.2% compounded monthly?

If Kelly can make monthly payments of $725 for 20 years, how much money could she borrow at 6.9% compounded semi-annually?

Dave Bidini has saved $20,000 for a down payment on a home and plans to save another $5,000 at the end of each year for the next five years. He expects to earn 7.25% compounded annually on his savings. How much will he have in five years' time? (Taken from CIFP course materials.)

A lottery offers the winner the choice between a $150,000 cash prize or month-end payments of $1,000 for 12½ years, increasing to $1,500 per month for the next 12½ years. Which alternative would you choose if money can earn 8.25% compounded monthly over the 25-year period?

Sam has two offers to buy his is motorcycle. The first offer is a cash price of $15,000. The second offer is a down payment of $5,000, and quarterly payments of $725 for four years. If his money can earn 5.5% compounded quarterly, which option should Sam choose? What is the economic advantage?

Sam is saving $100 per month. How much will he have in his account at the end of five years if his account earns 3.8% compounded quarterly?

If $500 is deposited into an investment at the end of every month for five years and the money is then left to accumulate without any more deposits for another five years, what will be the total value of the investment if it earns a rate of 8% compounded quarterly?

Sharon wishes to have $30,000 in 4 years' time. If she deposits a lump sum of $3,500 now, then what monthly deposits need to be made if interest is at 2.7% compounded annually?

A Province of Ontario bond has 14½ years remaining until it matures. The bond pays $231.25 interest at the end of every six months. At maturity, the bond repays its $5,000 face value in addition to the final interest payment. What is the fair market value of the bond if similar provincial bonds are currently providing investors with a return of 3.8% compounded semi-annually?

Marika has already accumulated $18,000 in her RRSP. If she contributes $2,000 at the end of every six months for the next 10 years, and $300 per month for the subsequent five years, what amount will she have in her plan at the end of the 15 years? Assume that her plan will earn 9% compounded semi-annually for the first 10 years and 9% compounded monthly for the next five years.

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