Exam 12: Ordinary General Annuities

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?

A 22-year mortgage is amortized by payments of $1761.50 made at the end of each month. If interest is 9.65% compounded semi-annually, what is the mortgage principal?

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?

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.

What is the accumulated value of deposits of $1120.00 made at the end of every six months for three years if interest is 8.48% compounded quarterly?

Note: The calculations for this question were done using Excel's RATE function. A $345 000.00 mortgage is repaid in 19 years by making monthly payments of $2486.44. What is the nominal annual rate of interest compounded semi-annually?

You make 6 quarterly deposits starting at $135 and increasing at a constant rate of 4.5%. The interest rate is 8.4% compounded quarterly. What is the size of the last deposit?

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, when the plant is producing electricity. During the 60 years of production life of the plant, the operator will put $1 million at the end of the month in a savings account, earning 7.25% compounded semi-annually. At the end of the production life of the plant, there are no more contributions and the money is expected to grow at the rate of 6% compounded quarterly for the next 30 years. What will be the value of the decommissioning fund in 2120?

Knowing that the education costs for her kids would be huge, Roberta puts lump sum money from her inheritance in a savings account paying an interest of 4.69% compounded semi-annually. If ordinary annuity payments of $1500.00 per month are to be paid out of the account at the end of each month for four years, how much did Roberta deposit?

Sam took a $5000 loan to build a deck in the backyard. The loan requires payments at the end of each quarter or 4 years. If the interest on the loan is 9% compounded monthly, what is the size of each payment Sam is required to make?

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. What will be the size of his payments per month from the ordinary annuity for 20 years following his retirement?

How much should you invest today into account paying 3.2% compounded quarterly if you want to be able to withdraw at the end of every 3 month the amounts of money growing at a constant rate of 3% for the period of 5 years , if the first withdrawal is to be $100 five years three months from now?

What is the principal from which $279.00 can be withdrawn at the end of each month for 17.5 years if interest is 5.44% compounded quarterly?

A $360 000.00 mortgage is amortized by making monthly payments of $2600. If interest is 7.5% compounded semi-annually, what is the term of the mortgage?

Calculate the nominal interest rate of interest compounded quarterly if a loan of 43 000.00 is repaid in seven years by payments of $4000.00 made at the end of every six months.

Woods has contributed $3600.00 per year for the last ten years into a RRSP account earning 9% compounded semi-annually. His wife Karen, on the other hand, contributed $300 at the end of every month for the same period into a RRSP account earning 9% compounded quarterly. Who has bigger saving at the end of 10 years and by how much?

If a loan was repaid by monthly payments of $9230.00 in 7.5 years at 6.15% compounded annually, how much interest was paid?

How many deposits of $6100.00 made at the end of every 6 months are needed to accumulate to $172 000.00 at 5.24% compounded quarterly?

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?

Momin plans to buy a house on cash instead of paying mortgage. He plans to set aside $14 400 at the end of each year for 15 years. He puts his savings in a Tax Free Savings Account (TFSA)and invests them in a high risk mutual fund, which has traditionally earned 12.2% annually. Money decreases in value by 2.5% per annum as well. How long will it take Momin to reach his target?