Exam 3: Simple Annuities

Gary has determined he wants an annuity paying $10,000 a year for 10 years,with the first payment payable on his 60^th birthday.If j₁ = 8%,what single deposit must he make on his 40^th birthday to fund this annuity?

A company has developed a unique way to allow their employees to accumulate $5000 in order to buy $5000 worth of shares in the company.The company will set up an account for each employee,paying interest at j₁₂ = 12%.At the end of every month the company will deduct an amount from an employee's pay and deposit it into this account (first deduction made 1 month from now).The company has decided to deduct n-payments of $81.25,plus make a smaller concluding deduction one month after the final deduction of $81.25,at which time the employee will have $5000.What is the size of this smaller concluding deduction?

Sally deposits $10,200 today in a fund earning interest at j₂ = 6%.She wishes to withdraw $600 every 6 months for as long as possible,with the first withdrawal made today.Including the withdrawal made today,how many full withdrawals of $600 would she be able to make?

Sally can buy some furniture for $11,000 cash or monthly payments of $1000 for 1 year,with the first $1000 payment made today.What range contains the interest rate j₁₂ that Sally is being charged?

Jerry makes semi-annual deposits of $R into a fund paying j₂ = 5%.His first deposit was made on March 15,2011.His last deposit will be made on March 15,2015.On September 15,2015 he has accumulated $15,000 in the fund.What is R?

Betty,who just turned 17 today,receives an inheritance of $A.She will receive $5000 every 6 months for 10 years,starting the day she turns 25.If j₂ = 8%,what is A?

Bank A offers you a loan which you will repay over 5-years at j₁₂ = 6% with monthly payments of $1500.Bank B offers you the same loan amount,but at j₄ = 6%,which you will repay over 5-years with quarterly payments of $R.What is the maximum value of R for you to even consider Bank B?

Deposits of $2000 are made every 6-months for 6-years in a fund that pays interest at j₂ = 8%.Just after the 12^th deposit,the interest rate changes to j₄ = 8% and quarterly deposits of $1000 are now made,first deposit 3 months after the interest rate change.How much is in the fund immediately after the 20^th deposit of $1000?

An individual buys $15,000 worth of furniture.They make a down payment of $5000 and pay off the rest of their bill with quarterly payments of $R for 10 years.If j₄ = 8% and the first quarterly payment is made 3 months after the loan is advanced,what is R?

An investor wants to accumulate $10,000 at the end of 15 years by making 11 annual deposits of $R,1^st deposit to be made at the end of year 4.If j₁ = 7%,what is R?

Mrs.Smith makes 20 annual deposits of $2000 into a retirement savings account,first deposit made today.If she earns j₁ = 5% on her money,how much does she have 25 years from today?

A deposit of $10,000 is made today.Semi-annual withdrawals of $R are made for 15-years,first withdrawal made 6-months from today.The fund earns interest at j₂ = 10% for the first 6-years and j₂ = 6% thereafter.What is R?

A company wishes to accumulate $100,000.To do so,they will make quarterly deposits of $4000 into a fund paying interest at j₄ = 8%.It turns out they need to make 20 deposits,plus a smaller drop payment.What is the size of the drop payment needed?

You plan to make 40-quarterly deposits into a fund in order to have $10,000 at the end of 10 years.Consider the following 3 cases: a. Deposit $R_I starting today;earn j₄ = x% b. Deposit $R_II starting 3-months from today;earn j₄ = x% c. Deposit $R_III starting 3-months from today;earn j₁₂ = x% Which of the following is true?

You make quarterly deposits of $500.The first 12 deposits earn j₄ = 6%.Immediately after the 12^th deposit,the interest rate changes to j₄ = 4%.How much have you accumulated immediately after the 20^th deposit?

You deposit $100 every three months for the next 50 years,first deposit made today.If the interest rate is j₄ = 10%,how much do you have three months after your last deposit?

A payment of $25,000 is due on January 1,2014.To accumulate enough money to make this required payment,monthly deposits of $R were made into an account earning j12 = 6% starting on June 1,2012.If the last deposit is made on January 1,2014,what is R?

Trish needs to have $20,000 one year from now.She plans to make 9 equal monthly deposits,first deposit made today.What is the size of each deposit needed if the money is deposited into an account paying j₁₂ = 6%?

To buy some furniture,you can put $150 down and "don't pay a cent" for 6 months.At the end of 6 months,you begin making monthly payments of $100 for 2-years.If j₁₂ = 8.4%,what is the equivalent cash price of the furniture?

A loan of $10,000 is taken out today and is to be repaid over 2-years with weekly payments of $R at j₅₂ = 10.4%,first payment one week from today.What is R?