Exam 12: Ordinary General Annuities

Calculate the accumulated value after twenty years of payments of $12 000.00 made at the end of each year if interest is 6% compounded semi-annually.

What annually compounded rate of return must Thiva earn in her TFSA account in order for month end contributions of $950 to accumulate $1 million after 25 years?

Dion is planning to buy a brand new BMW. He plans to keep the car for 3 years and then trade it in. He borrows $37 000 at 7.2% compounded semi-annually to purchase the car. What monthly payment will reduce the balance on the loan after 3 years to the expected trade-in value of $16 500?

You can buy a piece of equipment for $8600. The equipment is expected to last for 9 years and you want to have it completely paid off 3.5 years before it becomes unusable. Current loan rates are 9.5% compounded annually. What is the size of your semi-annual payment?

A mortgage requires payments of $4000.00 at the end of every six months for twelve years. If interest is 8% compounded quarterly, calculate the principal of the loan.

What is the payment size of a loan that has semi-annual payments and an interest rate of 5.52% compounded monthly? The loan principal is $1641.12 and the loan is for 48 months.

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

Calculate the amount of money that must be deposited at the end of every month into an account paying 12% compounded annually to accumulate to $100 000.00 in ten years.

Edward Martin borrowed $15 810.00 from his uncle to finance his graduate studies. The loan agreement calls for equal payments at the end of each month for 6 years. The payments are deferred for 3 years and interest is 8.12% compounded semi-annually. What is the size of the monthly payments?

Bhamani is contributing to a RESP they have set up for their grandchildren. What amount will they have in the RESP after 13 years of contributing $185 at the end of every month if the plan earns 5.5% compounded quarterly?

You won $250 000.00 in a lottery and you want to set some of that sum of money aside for 11.5 years. After 11.5 years, you would like to receive $4500.00 at the end of each month for 4.75 years. If the interest is 6.79% compounded annually, how much of your winnings must you set aside?

How much must be deposited at the end of each month for 10 years to accumulate to $100 000.00 at 6.00% compounded yearly?

Jordan is considering building a nuclear power plant, which will be ready for production in 2030. The country's governing body is also considering a decommissioning liability law for the operator to put aside $1 million every month towards decommissioning cost. If the production life of the plant is 60 years and the operator puts the money at the end of the month in a savings account, earning 7.25% compounded semi-annually, what will be the value of the decommissioning fund after 60 years of production?

Don turned 60 years old today and has retired from Hydro One. Current economic value of his pension is his significant asset. He will be receiving pension payments of $7000 at the end of each month. Based on a 22-year life expectancy and money worth 8% compounded semi-annually, calculate the current economic value of Don's pension.

Siri plans to retire when her simple annuity savings account has enough money to receive $10 000.00 per month for twenty years starting at the end of the first month after her retirement. She starts saving $4420 per month. Calculate when should Siri retire from today if her savings account pays 4.9% compounded semi-annually.

Note: The calculations for this question were done using Excel's RATE function. Compute the nominal annual rate of interest on a loan of $67 000.00 repaid in semi-annual installments of $6540.00 in 11.5 years.

Saba gets a year-end bonus in December every year before the Christmas. She plans to invest $1000 from the bonus at the end of every year into mutual funds RRSP, which are expected to grow at the rate of 8% compounded semi-annually. What will be the total value of her periodic investments after 25 years?

What is the accumulated value after 11.25 years of monthly deposits of $415.00 earning interest at 5.56% compounded semi-annually if the deposits are made at the end of each month?

Calculate the accumulated value after ten years of payments of $1000.00 made at the end of each year if interest is 6% compounded monthly.

A $ 120 000.00 mortgage is amortized over 25 years. If interest on the mortgage is 8.5% compounded semi-annually, calculate the size of monthly payments made at the end of each month.