Exam 10: Annuities: Future Value and Present Value

A preferred share pays a dividend of $3.25 per quarter until it is redeemed, at which time the value of the share is $60. What is the fair market value of the share if the redemption date is in 10 years, and shares of this type are currently generating a rate of return of 8% compounded semi-annually?

If $1,000 per month is invested at 12% compounded monthly for the first three years and 16% compounded monthly thereafter, what will be the accumulated amount immediately after the 120^th investment. The first investment will be made one month from now.

Amanda is considering one of two options. The first option is to receive $48,000 now. The second option is to receive $75,000 at the end of the fifth year. Determine which option should be chosen to maximize benefits now given an interest rate of 8.8% compounded annually.

C&D Stereo sold a stereo system on a plan that required no down payment and nothing to pay until January 1 (four months away). Then the first of 12 monthly payments of $226.51 must be made. The payments were calculated to provide C&D Stereo with a return on the account receivable of 16.5% compounded monthly. What was the selling price of the stereo system?

Sebastin has made contributions of $2,000 to his RRSP at the end of every six months for the past eight years. The plan has earned 5.5% compounded semi-annually. He has just moved the funds to another plan, paying 4% compounded quarterly. He will now contribute $1,500 at the end of every three months. What total amount will he have in the plan seven years from now?

Determine the current economic value of a 25-year annuity providing $10,000 per year for the first 10 years, $15,000 for the next 10 years and $25,000 for the last 5 years, given an interest rate of 6.3% compounded annually.

Fred made 12 end-of-month deposits of $250 into a mutual fund earning 16% compounded monthly. How much will he have in his account two years after his last deposit if the fund continues to earn 16% compounded monthly?

The winner of a "Ten-million dollar" lottery prize is actually entitled to payments of $33,333.33 at the end of every month for 25 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 8.1% compounded monthly. What would be the amount of the single payment?

Determine the future value:

You have received two offers on the used car you wish to sell. Mr. Lindberg is offering $9500 cash, and Mrs. Martel's offer is five semi-annual payments of $2,000 including one on the purchase date. Which offer has the greater economic value using a discount rate of 5% compounded semi-annually? What is the economic advantage in current dollars of the preferred alternative?

Imperial Life Inc. is quoting a rate of return of 5.2% compounded quarterly on 15-year annuities. How much will you have to pay for a 15-year annuity that pays $5,000 (at the end of) every three months?

At the end of every year for 45 years Sabrina invested $500 into her retirement plan. The plan has earned 13% compounded annually over the 45 years. She made the last deposit today. How much money has she accumulated?

An investment plan requires year-end contributions of $1,000 for 25 years. What will be the future value of the plan if it earns 7½% compounded monthly for the first 10 years and 8% compounded semi-annually thereafter?

A loan at 6% compounded semi-annually requires equal monthly payments. What is the value of c? What is the approximate value of the periodic interest rate for one payment interval? Will the correct value be larger or smaller than your estimate? Explain.

Quarterly contributions of $700 are made to an RRSP that earns 6% compounded monthly. How much will be in the plan immediately after the twentieth deposit?

What price will a finance company pay for a conditional sale contract requiring 15 monthly payments of $180.50 if the company requires a rate of return of 21% compounded semi-annually? The first payment is due one month from now.

Classify the type of annuity described in the following scenario. A student loan carrying interest of 2.5%, compounded quarterly is repaid with payments of $1000 at the end of every three months.

An investment consists of deposits of $500 per quarter for 10 years. How much will be in the account after 10 years if interest is 5.5% compounded semi-annually?

Assume two investments can earn 6.4% compounded annually. Determine how much larger an investment with consistent annual contributions of $3,000 be over 20 years, versus an investment where no payments are made for the first 5 years and annual contributions of $4,000 per year for the remaining 15 years.

What distinguishes a General Annuity from an Annuity Due?