Exam 10: Annuities: Future Value and Present Value

Calculate the difference in the current economic values of the following two annuities: #1: Payments of $300 made at the end of every month for the next five years. #2: Payments of $200 made at the end of every month for the next 10 years. Use an interest rate of 14.4% compounded monthly for both annuities.

Morgan has decided to make contributions of $250 to her Retirement Savings Plan (RSP) at the end of each month for 30 years. She anticipates that her RSP will earn 12.75% compounded monthly. She is 20 years old now and therefore he will be only 50 when this plan is completed. How much money will be in her RSP when she is 50 years of age?

What amount will be required to purchase a 20-year annuity paying $2,500 at the end of each month if the annuity provides a return of 6.75% compounded annually?

Jane is making monthly payments of $450 for four years for a car at an interest rate of 5.5% compounded semi-annually. What was the purchase price of the car?

A guaranteed contract entitles Jon to receive $525 at the end of every six months for the next nine years plus an additional single payment of $10,000 in nine years. If Jon sells the contract to The Corleone Finance Company now, for a price that would provide Corleone with a rate of return of 7.4% compounded semi-annually, what would that price be?

Your client has the following choices for an insurance benefit: She can receive $2,000 at the end of each year for the next five years or one "lump" sum today. If the current interest rate is 4.5% compounded annually, what lump payment today is equivalent to the five payments? (Taken from CIFP course materials.)

Dakota intends to save for occasional major travel holidays by contributing $275 at the end of each month to an investment plan. At the end of every three years, she will withdraw $10,000 for a major trip abroad. If the plan earns 6% compounded monthly, what will be the plan's balance after seven years?

What is the appropriate price to pay for a contract guaranteeing payments of $1,500 at the end of each quarter for the next 12 years? You require a rate of return of 6% compounded quarterly for the first five years and 7% compounded quarterly for the next seven years.

François and Pat wish to structure the payments from a 20-year annuity so that the end-of-quarter payments increase by $500 every five years. Maritime Insurance Co. will pay 5% compounded quarterly on funds received to purchase such an annuity. How much must François and Pat pay for an annuity in which the quarterly payments increase from $2,000 to $2,500 to $3,000 to $3,500 in successive five-year periods?

Determine the present value of the ordinary annuity:

Leona contributed $3,000 per year to her RRSP on every birthday from age 21 to age 30 inclusive. She stopped employment to raise a family and made no further contributions. Her husband, John, started to make annual contributions of $3,000 to his RRSP on his 31^st birthday and plans to continue up to and including his 65^th birthday. Assuming that both of their plans earn 8% compounded annually over the years, calculate and compare the amounts in their RRSPs at age 65.

What amount would you have to invest now at 10% compounded semi-annually in order to make withdrawals of $3,500 every half-year for eight years? The first withdrawal is to be made in six months.

If money can earn 6% compounded monthly, how much more money is required to fund an ordinary annuity paying $200 per month for 30 years than to fund the same monthly payment for 20 years?

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

Amanda purchased $25,000 vehicle through Mazda's Graduate Program. She would pay monthly payments over 5 years, at a rate of 2.8% compounded monthly. At the end of the third year, Amanda wished to pay off her loan outright. Determine the Balance on the loan at the end of year 3.

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

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

Determine the present value of the ordinary annuity:

Juliana has $54,500 in her "World Tour Savings Plan" right now. She will not be able to make any more contributions to the Plan but she is planning to let the money accumulate until she has enough so that he can take out $2,500 per month for 3 years while she travels around the world. She will take out the first $2,500 one month after she leaves on her trip. If her investments earn 9.9% compounded monthly, how many months will it be before she leaves on her trip?

Determine the future value