Exam 11: Annuities: Periodic Payment, Number of Payments, and Interest Rate

Calculate the periodic payment for the following ordinary annuity.

We plan to have $1,500,000 in 35 years. We will make quarterly deposits of $1,000 at the end of every 3 months for 25 years and then allow the money to accumulate, without more deposits, at 8% compounded annually for the last 10 years. What compounded annual nominal rate of return will we have to earn over the 25 years that we will be making the quarterly deposits?

Heather's investments will earn 11% compounded annually and, in 30 years, she must have $645,000. For the next 20 years she can make year-end contributions of $10,000. She will not be able to make any contributions after 20 years from now. She wants to know if she has to start the $10,000 annual contributions now in order to reach her goal. If not, how many years can she wait before starting the $10,000 annual contributions?

What annual deposit should Martina make to her RRSP at the end of every year if the funds earn 12% compounded monthly and her goal is to accumulate $1,000,000 at the end of 25 years?

For $100,000, Royal Life Insurance Co. will sell a 20-year annuity paying $802.76 at the end of each month. What monthly compounded nominal rate and effective rate of return does the annuitant (the buyer of the annuity) earn on the invested funds?

Aden is scheduled to make a lump payment of $25,000, 11 months from now, to complete a real estate transaction. What end-of-month payments for the next 11 months should the vendor be willing to accept instead of the lump payment if he can invest the funds at 5.4% compounded monthly?

A $10,000 deposit along with quarterly contributions of $150 accumulates to $18,000 in 5 years. Determine the nominal rate of interest if interest is compounded annually.

If $300,000 is used to purchase an annuity earning 4.5% compounded monthly and paying $2,500 at the end of each month, what will be the term of the annuity? Include the final, smaller annuity payment in the total.

After 15 years of contributions of $3,500 at the end of every six months to a Retirement Savings Plan, the accumulated amount stood at $232,536. What semi-annually compounded nominal rate of return was earned by the funds in the RSP?

Calculate the term, expressed in years and months, of the following ordinary annuity.

Calculate the term, expressed in years and months, of the following ordinary annuity.

Sandy is planning to accumulate $500,000 after 30 years by making investments of $300 at the end of each month for 20 years and leaving the money to grow at 7% compounded semi-annually for 10 more years. What monthly compounded nominal rate will Sandy have to be earning over the 20 years that she makes the monthly deposits?

Farah has $600,000 in her RRSP and wishes to retire. She is considering using the funds to purchase an annuity that earns 5% compounded annually and pays her $3500 at the end of each month. If she buys the annuity, for how long will she receive payments?

A loan of $25,000 is to be repaid by monthly payments of $400. The interest rate is 9% compounded monthly. How many months will it take for the amount owing on the debt to be reduced to less than $10,000?

An annuity purchased for $175,000 pays $4,000 at the end of every quarter. How long will the payments continue if the funds earn 7% compounded semi-annually?

Calculate the periodic payment for the following ordinary annuity.

What monthly compounded nominal rate of return would one need to achieve in order to have investments of $100 made at the end of every month for 35 years to accumulate to $1 million?

How much longer will it take month-end RRSP contributions of $500 to accumulate $500,000 than month-end contributions of $550? Assume that the RRSP earns 3.75% compounded monthly. Round the time required in each case to the next higher month.

A major daily newspaper charges $260 (paid in advance) for an annual subscription, or $26 per month payable at the end of each month to the carrier. What is the effective interest rate being charged to the monthly payment subscribers?

Ernie's Electronics sells an LED HD television priced at $2395 for $100 down and payments of $100 per month, including interest at 9.6% compounded monthly. How long after the date of purchase will the final payment be made?