Exam 10: Annuities: Future Value and Present Value

A seven-year capital lease of an executive jet requires semi-annual payments of $200,000 at the beginning of each six-month period. The company can borrow funds for seven years at 7.4% compounded semi-annually. a. What long-term lease liability will the firm set up at the start of the term of the lease? b. What liability will remain halfway through the term of the lease

An annuity contract pays $2,000 semi-annually for 15 years. What is the present value of the annuity six months before the first payment if money can earn 6% compounded semi-annually for the first six years and 10% compounded semi-annually for the next nine years?

Kent sold his car to Carolynn for $2,000 down and monthly payments of $295.88 for 3½ years, including interest at 7.5% compounded monthly. What was the selling price of the car?

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

Jennifer already has $15,500 saved for a down payment for a house and she plans to save another $400 at the end of each month for the next three years. If she earns 8.4% compounded monthly how large will her down payment be in three years?

Determine the present value of the ordinary annuity:

How much larger will the value of an RRSP be at the end of 20 years if the contributor makes month-end contributions of $500 instead of year-end contributions of $6,000? In both cases the RRSP earns 4.5% compounded semi-annually.

Manuel purchased a boat for $2,000 down with the balance to be paid by 36 monthly payments of $224.58 including interest at 10% compounded monthly. a) What was the purchase price of the boat? b) What is the balance owed just after the ninth payment?

Dr. Krawchuk made deposits of $2,000 to his RRSP at the end of each calendar quarter for 6 years. He then left general practice for specialist training and did not make further contributions for 2½ years. What amount was in his RRSP at the end of this period if the plan earned 5% compounded quarterly over the entire 8½ years?

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?

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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

This problem demonstrates the dependence of the future value of an annuity on the interest rate. Suppose $1,000 is invested at the end of each year for 20 years. Calculate the future value if the investments earn an annually compounded rate of return of: a) 5% b) 6% c) 7% d) 8% Note that the future value increases proportionately more than the interest rate.

How much more will you have in your RRSP 30 years from now if you start to contribute $1,000 per year at the end of this year instead of waiting five years to begin contributing $1,000 at each year-end? Assume that the funds earn 8% compounded annually in the RRSP.

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 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?

What is the value of a contract that will pay $500 at the end of each month for 2 years and $2,000 at the end of each quarter for the subsequent 3 years? Use a discount rate of 6% compounded semi-annually.

Determine the present value of the ordinary annuity:

An ordinary annuity consists of 25 annual payments of $1,000. Calculate its future value if the funds earn: a) 6% compounded annually. b) 6% compounded quarterly. c) 6% compounded monthly.

The monthly payments on a five-year loan at 7.5% compounded monthly are $200.38. a) What was the original amount of the loan? b) What is the balance after the 30^th payment?