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Exam 12: Ordinary General Annuities

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Question 1

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Silva is contemplating to buy a 20 year annuity paying $2500 at the end of each month. What amount will be required to purchase the annuity, if the annuity provides a return of 6.75% compounded annually?

A) $334 000
B) $47 246
C) $600 000
D) $37 037
E) $567 436

F) A) and B)
G) None of the above

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Question 2

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Sean Paul borrowed $20 000.00 from his father to finance his new business. The loan agreement calls for equal payments at the end of each month for 10 years. The payments are deferred for 4 years and interest is 4.00% compounded semi-annually. What is the size of the monthly payments?

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Balance in 4 years: i = 0.04 ÷ 2 = 0.02, n = 4 × 2 = 8 FV = 20 000 11eaae09_72fd_41ac_bb34_cb14fcdae947_TB3016_11 = $23433.19 = 11eaae09_72fd_41ad_bb34_695ef44b577a_TB3016_11 For annuity: i = 0.02, n = 10 × 12 = 120, c = 11eaae09_72fd_68be_bb34_c90ad2af766f_TB3016_11 = 11eaae09_72fd_68bf_bb34_0baac17cfc5c_TB3016_11 p = 11eaae09_72fd_68c0_bb34_b3828c978757_TB3016_11 - 1 = 0.0033058903 23433.19 = PMT 11eaae09_72fd_68c1_bb34_85163a9d2e17_TB3016_11 23433.19 = PMT(98.9230334) $236.88 = PMT

Question 3

Multiple Choice

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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?

What is the accumulated value after 15.50 years of deposits of $500.00 earning interest at 4.00% compounded semi-annually if the deposits are made at the end of each quarter?

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?

Mr. Sepaba accumulated $600 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $3000.00 at the end of every month from the fund. If interest is 4.5% compounded yearly, for how long can Mr. Sepaba make withdrawals?

How much must be deposited at the end of each quarter for 5 years to accumulate to $27 000.00 at 6.84% compounded monthly?

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?

If a student loan was repaid by monthly payments of $800.00 in 5.0 years at 8.00% compounded yearly, how much interest was paid?

Momin plans to buy a house on cash instead of paying mortgage. He targets spending $400 000 on his dream house. He plans to set aside $1200 every month to reach his target. 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. How long will it take Momin to reach his target?

You are to receive $16 700 from your trust fund in 7.5 years. You negotiate a deal where you can withdraw $350 per month starting 2.75 years before you can withdraw the remainder of the funds. You are able earn 4.18% compounded annually on your money. How much is your trust fund reduced to?

For how long will Jessica have to make payments of $1200.00 at the end of every three months to repay a loan of $10 000.00 if interest is 12% compounded semi-annually?

Siri plans to retire in 18 years and would like to receive $10 000.00 per month for twenty years starting at the end of the first month after her retirement. Calculate the amount he must invest now every month (at the end of the month) if interest is 4.9% compounded semi-annually.

A loan of $91 450.00 is to be repaid by equal semi-annual payments for 11 years. What is the size of each semi-annual payment if the interest is 9.24% compounded annually?

Note: The calculations for this question were done using Excel's RATE function. A property worth $15 000.00 is purchased for 10% down and semi-annual payments of $1750.00 for twelve years. What is the effective rate of interest if interest is compounded semi-annually?

A real estate developer bought land for $170 000.00 down and monthly payments of $10 450.00 for 5 years. What is the equivalent cash price if money is worth 7.75% compounded semi-annually?

Calculate the amount of money that must be deposited at the end of every three months into an account paying 6% compounded monthly to accumulate to $12 500.00 in ten years.

Sam got a job at the Brick. He plans to save $500 every month for 3 years to buy a car. The savings account earns 2.25% compounded semi-annually. If he puts the money in his savings account at the end of each month, what will be the balance in the account at the end of the three-year term?

You buy a motorcycle for $52 523 plus freight of $724 and other delivery charges of $561. You have saved 25% of the total purchase price towards a down payment. The bank is willing to finance the purchase of the motorcycle at 9.86% compounded quarterly. What is the size of your monthly payment if the loan is for 4.5 years?

Sam got a job at the Brick. He plans to save $500 every month for 3 years to buy a car. The savings account earns 2.25% compounded semi-annually. If he puts the money in his savings account at the end of each month, what will be the present value of the balance in the account at the end of the three-year term?