Exam 10: Annuities: Future Value and Present Value

A 20-year mortgage requires payments of $1194.85 per month at an interest rate of 7.8% compounded monthly? What was the amount of the mortgage?

Determine the future value:

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

Calculate the future value of investments consisting of payments of $800 at the end of each calendar quarter for seven years. The rate of interest earned will be 7% compounded quarterly for the first 30 months and 6% compounded semi-annually for the remainder of the annuity's term.

What amount would you have after 10 years by investing $500 at the end of every month if your investment earns 14% compounded quarterly?

Calculate the equivalent periodic interest rate per payment interval for the following annuity: Semi-annual payments earning 11% compounded quarterly.

Acme class B preferred shares pay quarterly dividends of $2.50. The shares must be redeemed at $100 by Acme 10 years from now when the last dividend is paid. At what price should the shares trade today if the rate of return required by the market on similar preferred shares is 12% compounded quarterly?

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?

Determine the present value of the ordinary annuity:

Joshua wants to structure a 20-year annuity so that its end-of-quarter payments are $2,000 for the first 10 years and $2,500 for the next 10 years. Pacific Life Insurance Co. offers to sell this annuity with a 4.8% compounded monthly rate of return to the annuitant. What amount must Joshua pay to Pacific for the annuity?

The sale of a $30,000 vehicle is to be financed through monthly payments over a 5-year period at an interest of 4.4% compounded monthly. Determine how much will be saved if payments were made at the beginning of each month compared to the end of the month over this time period.

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

Samuel has $290,000 in his Registered Retirement Savings Plan right now. He will not be able to make any more contributions to the RRSP but he is planning to let the money accumulate until he has enough so that he can take out $3,000 per month for 25 years. How long will he have to wait until he takes out the first $3,000 withdrawal? His investments earn 7.5% compounded monthly.

How much money would you have at the end of five years if you made deposits of $450 at the end of every month into an investment that accumulated at 18% compounded monthly?

Hank Toms is going to start his Retirement Savings Plan (RSP) by depositing $2,500 at the end of every six months for 20 years. Also, seven years from now, he is going to receive the $45,000 proceeds from a trust fund that will go directly into the RSP at that time. If his Plan earns 12% compounded monthly, how much money will Hank Toms have in the RSP in 20 years?

The Johnston family wish to purchase a $350,000 condo. The borrowing rate is set at 3.95% compounded quarterly based on a 25-year period. Determine how much money will be saved if their monthly payments are at the start of each month instead of at the end of the month.

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.

What is the maximum price you should pay for a contract guaranteeing month-end payments of $500 for the next 12 years if you require a minimum rate of return of at least 8% compounded monthly for the first five years and at least 9% compounded monthly for the next seven years?

How much larger will the value of an RRSP be at the end of 25 years if the RRSP earns 9% compounded monthly instead of 9% compounded annually? In both cases a contribution of $1,000 is made at the end of every three months.