Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

What is the discounted value of deposits of $570.00 made at the beginning of every three months for 8.25 years if money is worth 8.4% compounded quarterly?

Determine the accumulated value after 13.5 years of deposits of $470.00 made at the beginning of every three months and earning interest at 7.2% compounded quarterly.

Jamal plans to retire in 17 years. He is saving $2000 every start of the month in a retirement savings account paying him a long-term interest of 9% compounded quarterly. What will be the size of his payments at the start of each month from the annuity for 20 years following his retirement?

Note: The calculations for this question were done using Excel's RATE function. A vacation property valued at $62 000.00 was bought for 40 payments of $2150.00 due at the beginning of every six months. What nominal rate of interest was charged?

The monthly rent payment on computer equipment is $30.00 payable in advance. What yearly payment in advance would satisfy the lease if interest is 12% compounded monthly?

Jamal plans to retire in 17 years. He is saving $2000 every start of the month in a retirement savings account paying him a long-term interest of 9% compounded quarterly until retirement. The rate changes following the retirement. He wants $7000 per month paid to him at the start of the month for 20 years after the retirement. At what rate should his savings account pay him to fulfill his dream? (Use the Rate function in Excel)

Dell Canada advertises a computer bundle including printer, router and home network attached storage for $2995. The same system bundle may be leased for 24 months at $130 per month, at the beginning of each month. At the end of the lease, the bundle may be purchased for 10% of its retail price. What is the economic cost of the lease or purchase in present value, if a two year loan can be obtained at 12% compounded annually to purchase the computer?

Jamal plans to retire in 17 years. He is saving $2000 every start of the month in a retirement savings account paying him a long-term interest of 9% compounded monthly. What will be the size of his payments at the start of each month from the ordinary simple annuity for 20 years following his retirement?

Determine the accumulated value after 14.5 years of deposits of $172.00 made at the beginning of every 6 months and earning interest at 4.45% compounded monthly?

Starting in 5 years you want to be able to withdraw $6220 every six months for 7.5 years. You want to deposit a single amount immediately and then let it grow at a rate of 4.88% compounded quarterly. How much do you have deposit?

A rental property provides a monthly income of $1472.00 due at the beginning of every month. What is the cash value of the property if money is worth 7.32% compounded monthly?

A sum of money is deposited at the end of every 6 months for 9.5 years at 8% compounded semi-annually. After the last deposit, interest for the account is to be 4.5% compounded quarterly and the account is to be paid out by making payments of $4360.00 at the end of each month over 7.75 years. What is the size of the semi-annual deposit?

A fund to provide an annual scholarship of $5700.00 is to be set up. If the first payment is due in three years and interest is 6.4% compounded quarterly, what sum of money must be deposited in the scholarship fund today?

Equal sums of money are withdrawn monthly from a fund of $60 000.00 for 15 years. If interest is 12% compounded monthly, what is the size of each withdrawal if the withdrawal is made at the beginning of each month?

Jeff is retired and has an investment fund worth $210 000 in an RRSP, which earns 9% compounded semi-annually. He plans to withdraw only $2000 at the beginning of each month starting today. When will the fund become depleted?

How much does a depositor have to save at the beginning of every 6 months for eleven years to accumulate $17 448.00 if interest is 6.25% compounded semi-annually?

Mark contributed $270.00 at the end of every 3 months for 5.75 years into an RRSP earning 12.6% interest compounded quarterly. Four years after the last contribution he converted the RRSP into a RRIF that is to pay him quarterly payments for 29.5 years. If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 9.5% compounded quarterly, how much will Mark receive every 3 months?

Jack Chen makes deposits of $415.00 at the beginning of every three months. Interest earned by the deposits is 4.12% compounded quarterly. a)What will the balance in Jack's account be after eight years? b)How much of the balance will Jack have contributed? c)How much of the balance is interest?

National Research Council is considering the establishment of $2 million endowment held in perpetuity of a Visiting Professor chair at UOIT. The ongoing cost will be $12 500 at the end of each month. What monthly compounded nominal rate of return must be earned to fully fund the position?

Jessica bought a bedroom suite on credit, signing an installment contract with a finance company that requires monthly payments of $100.00 for 5 years. The first payment is made on the date of signing and interest is 24% compounded monthly. a)What was the cash price? b)How much will Tricia pay in total? c)How much of what she pays will be interest?