Exam 11: Ordinary Simple Annuities

Find the present value for payments of $500.00 made at the end of each quarter for ten years, if interest is 8% compounded quarterly.

Note: The calculations for this question were done using Excel's RATE function. What nominal rate of interest is paid on quarterly RRSP contributions of $573.00 made for 17.75 years if the balance just after the last contribution is $106 000.00?

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 monthly. 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?

Janice plans to retire in 10 years and would like to receive $3000.00 per month for fifteen years starting at the end of the first month after her retirement. Calculate the amount she must invest now if interest is 7.5% compounded monthly.

What is the nominal rate of interest if a six-year loan of $71 000.00 is repaid by monthly payments of $1701.58?

You are offered payments of $475 at the end of each semi-annual period for 6.5 years. You think that the cost of money is 6.14% compounded semi-annually. What is the present cash value?

Jason deposited $100.00 at the end of each month for five years into an account paying 6% compounded monthly. What will be the balance in the account at the end of the five-year term?

How much interest is included in the accumulated value of $4750 paid at the end of every six months for 4.5 years if the interest rate is 8.5% compounded semi-annually?

What is the term of a mortgage of $235 000.00 repaid by monthly payments of $2475.00 if interest is 7.55% compounded monthly?

What is the size of semi-annual deposits that will accumulate to $113 200.00 after 9.5 years at 6.5% compounded semi-annually?

Nuclear power plants are required to have full decommissioning costs accumulated during the useful life of the plant. The new nuclear plant at Darlington is designed for 60 years of operational life starting in 2025. OPG plans to set aside $1 million per month in a sinking fund for the operational of the plant. What is the value of the value of this sinking fund at the end of the plant life, if OPG expects an average rate of return of 2.5% compounded monthly?

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 monthly, what will be the value of the decommissioning fund after 60 years of production?

Mr. Hughes has contributed $4000.00 per year for the last ten years into a RRSP account earning 9.00% compounded annually. Suppose he leaves the accumulated contributions for another five years in the RRSP at the same rate of interest. a)How much will Mr. Hughes have in total in his RRSP account? b)How much did Mr. hughes contribute? c)How much will be interest?

You currently have $4000 saved towards the purchase of a new car. You want to be able to buy a car for $15000 in 4 years. Your money is earning 5% compounded yearly. What is the size of your yearly deposit?

On his retirement, Louis received a lump sum of $800 000 from his employer. Taking advantage of existing tax legislation, he invested his money in an annuity that provides for payments of $60 000 at the end of every 3 months. If interest is 6.25% compounded quarterly, how long will the annuity exist?

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 monthly 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 should his savings account pay him to fulfill his dream? (Use the Rate function in Excel)

How long will it take for quarterly deposits of $425 to accumulate to be $16440 at an interest rate of 8.48% compounded quarterly? (Final answer in years and months e.g., 7 years and 4.24 months)

$1000.00 is deposited at the end of every month into an account earning 6.00% compounded monthly. If the balance in the account five years after the last deposit is to be $50 000.00, how many deposits are needed?

When the conversion period is different from the payment period, an annuity is called:

Leanne Simon made ordinary annuity payments of $81.00 per month for fourteen years earning 9% compounded monthly. How much interest is included in the future value of the annuity?