Business Mathematics Study Set 1

Mathematics

Quiz 11 :

Annuities: Periodic Payment, Number of Payments, and Interest Rate

Quiz 11 :

Annuities: Periodic Payment, Number of Payments, and Interest Rate

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Heather is planning to invest a constant amount of money at the end of every year for 15 years and then allow her money to accumulate interest for 15 more years without any additional deposits. If her investments earn 11% compounded annually and she must have $650,000 in 30 years, how much will she invest at the end of each of the next 15 years?
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Answer:

E

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Fred must pay a $25,000 obligation one year from now. What end-of-month payments for twelve months would put the creditor in an equivalent financial position if the creditor can earn 9% compounded monthly?
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C

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If you have $45,000 earning 9.6% compounded monthly, how much money could you take out of the investment at the end of every year for 10 years?
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B

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What annual deposit should Martina make to her RRSP at the end of every year if the funds earn 12% compounded monthly and her goal is to accumulate $1,000,000 at the end of 25 years?
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Vince has $35,000 to purchase an annuity that will provide him with equal payments at the end of every three months for the next six years. If the funds earn 8% compounded quarterly, what is the size of the quarterly payments he will receive?
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How much will Clarence have to invest at the end of every year at 11% compounded annually if he is going to accumulate $25,000 in five years?
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The interest rate charged on a loan of $85,000 is 7.75% compounded annually. If the loan is to be paid off over seven years, calculate the size of the annual payments.
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An investment of $25,000 is made for a 10-year term. After the term expires, equal withdrawals will be made at the end of every month for 15 years. What will the size of the monthly withdrawal be if the investment earns 9% compounded monthly for both the deposit and withdrawal periods.
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What regular investment, made at the end of every three months and earning 10% compounded quarterly, would accumulate to $475,000 in 20 years?
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A 25-year annuity is purchased for $650,000. Determine the payments it will deliver on a quarterly basis if the rate of interest is 5.05% compounded monthly.
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Marvin hopes to accumulate $1,000,000 in his retirement plan by making equal contributions at the end of each month for 35 years. He is planning to earn 10.8% compounded monthly. What amount should he deposit every month?
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Calculate the size of the monthly mortgage loan payment if a $121,500 loan at 7% compounded semi-annually is to be paid off over 18 years.
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A loan of $17,200 at 9% compounded monthly is to be paid off by equal payments to be made at the end of every month for three years. What is the size of the monthly payment?
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If a single sum of $25,000 is invested at age 25 at 13% compounded annually, what amount will the investor be able to withdraw from the savings, at the end of every month for 20 years, beginning at age 65? At age 65 the investor will put his money into a safer investment that earns only 6% compounded monthly.
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Vanessa wants to retire in 25 years with enough saved to be able to withdraw $5,000 monthly for 20 years. She has already accumulated $48,000 in her investment account. Assume that the rate of interest is 4.8% compounded annually for the 25 years of her contributions, and changes to 3.6% compounded monthly for the next 20 years. Determine what annual contributions she has to make for the next 25 years in order to meet her objective.
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Today, Barry reached his 50th birthday and he has $70,000 in his retirement fund. His goal is to have $500,000 on his 65th birthday. He can expect his investments to earn 13% compounded semi-annually. How much will he have to invest at the end of every six months for the next 15 years in order to reach his goal?
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A loan of $45,000 calls for equal payments at the end of every three months for the next six years. What is the size of the payments if the interest rate is 14% compounded semi-annually?
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If the invested funds earn 13% compounded quarterly what amount invested at the end of every six months for 15 years will accumulate to $295,000?
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Given the time-value of money of 11% compounded annually, calculate the size of the month-end payments for the next five years that would be equivalent to a single payment of $13,285 payable five years from now.
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Sally has invested a constant amount at the end of every six months for the last 40 years. She has made wise investment decisions and has earned a return of 16.4% compounded semi-annually. Today the value of her savings has reached $2,500,000. What amount has she been investing every half-year?
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