Business Mathematics Study Set 1

Mathematics

Quiz 12 :

Annuities: Special Situations

Quiz 12 :

Annuities: Special Situations

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Hard Rock Paving Company is applying for a loan. It is your job to determine how much they will be able to borrow. They will not be making any payments for the first 15 months. After that, they will make payments of $1,000 per month for four years. There is no interest-free grace period. The first $1,000 payment will be made 15 months after the loan is received. If the interest rate is 13.2% compounded monthly, how much can they expect to borrow?
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B

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Heather is planning to retire in 10 years. She will then need an income of $1,500 at the end of every month for the subsequent 25 years. She is going to make one investment today to provide all of the money she will eventually collect. Her investments will earn 12% compounded monthly. How much should she invest today?
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A

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What is the economic value today of 24 monthly payments of $500 with the first payment occurring 10 months from today? Assume that money can earn 12% compounded monthly.
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Calculate the present value of a deferred annuity of 20 annual payments of $100,000 each The interest rate is 13.5% compounded annually and the first payment will be made 11 years from now.
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Fred intends to retire in 10 years. To supplement his pension, he would like to receive $500 every six months for 20 years. If he is to receive the first payment six months after the date of his retirement, what lump amount must he invest today to achieve his goal? Assume that the investment will earn 12% compounded semi-annually.
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Harold is planning to retire in 21 years. After that he will need an income of $4,500 at the end of every month for the subsequent 25 years. He is going to make one investment today to provide all of the money he will eventually collect. His investments will earn 9% compounded monthly. How much should he invest today?
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Mrs. O'Halloran gave $130,000 to the University of Northern British Columbia for a perpetual scholarship fund. What amount can be awarded on each anniversary if the scholarship fund earns 7% compounded annually?
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Andy deposits $40,000 into an account earning 6.6% compounded annually for 5 years. After this time, Andy wishes to withdraw $2,814.41 at the end of each quarter and have $10,000 remaining. Determine the number of withdrawals Andy can make.
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An individual wants to receive end-of-month payments of $1,200 for 20 years after she retires 15 years from now. What lump amount must she invest today to provide the retirement income? Assume the investment earns 7% compounded monthly for the entire 35 years.
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Gregory deposits a $30,000 for a period of time at a 3.5% rate of interest compounded semi-annually. The accumulated amount provides Gregory the benefit of withdrawing $1,165 at the end of each month for three years. Determine how long the initial deposit accumulated interest.
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Moses' goal, when he retires from work in seven years, is to have $400,000 in his Retirement Fund. Assuming he achieves his goal and the fund earns 7% compounded semi-annually after he retires, what is the amount that Moses will be able to take out of his Retirement Fund at the end of every six months for 25 years after he retires?
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Calculate the present value of a deferred annuity of 20 annual payments of $25,000 each The interest rate is 8.5% compounded annually and the first payment will be made in six years.
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What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?
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A purchase agreement for a $22,000 truck requires 60 equal payments every six months. If the first payment is due one year after the date of purchase and interest is charged at 18% compounded monthly, what is the size of each payment?
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Anita is planning to go back to school in 2 years. Once at school, she wishes to be able to withdraw $900 at the end of each month for 2 years. If interest is 4.5% compounded monthly, determine the amount that should be deposited now to fulfil her goal.
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Fred purchased a farm with a down payment of $8,500 and 48 semi-annual payments of $3,000. The first of these payments is to be made two years after the date of purchase. What was the purchase price of the farm if the interest rate charged on the balance is 14% compounded semi-annually?
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The Pithybottoms want to make a donation to set up a scholarship trust fund at Hinose College. The fund is to support payments of $5,000 at the end of every three months in perpetuity. If the fund earns 7.5% compounded quarterly, how much must they donate?
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What amount can be paid at the end of every month, in perpetuity, from an endowment of $75,000 earning 8% compounded monthly?
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Harry deposits $10,000 into an investment account that earns 7% compounded monthly. How many monthly withdrawals of $310 will he be able to make if his first withdrawal is exactly five years after his deposit?
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Evergreen Landscaping is applying for a loan. Your help is needed to determine how much they can borrow. They will not be able to make any payments for the first 18 months. After that, they will make payments of $750 per month for five years. There is no interest-free grace period. The first $750 payment will be made 18 months after the loan is received. If the interest rate is 10.5% compounded monthly, how much can they expect to borrow?
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