Exam 3: Simple Annuities

Cam has just won $1 million in the lottery.He plans to spend half of it now and invest the rest in an annuity that has semi-annual payments for the next 30 years,first payment 6 months from now.If money is worth j₂ = 8%,what is the size of the semi-annual payment?

Mrs.Gerri Atric decides to save money for her retirement.She makes monthly deposits of $150 starting on November 7,2012 and continuing to April 7,2015.If her deposits are earning j₁₂ = 8%,how much money will she have on April 7,2015?

The accumulated value of n payments of $500 at i immediately after the n^th payment is S.Which of the following gives the correct accumulated value immediately after the (n+2)^th payment of $500?

You deposit $3000 every 6-months into a fund earning interest at j₂ = 7%.Immediately after the 9^th deposit,the interest rate changes to j₂ = 6%.How much is in your fund immediately after the 20^th deposit?

Drew Wallace has made deposits at the end of each year into a registered savings account for the past 10 years,with his final deposit being made today.He deposited $2500 for the first 5 years and $2000 for the last 5 years.The account earned interest at j = 8%.How much is in his account today (just after his final deposit)? (answer to the nearest dollar)

To buy a car,you are given two options.Option 1 is to pay $20,000 cash today.Option 2 is to make monthly payments of $500 for as long as necessary,first payment made today.If the dealer charges interest at j₁₂ = 5.4%,how many payments are needed,including the very first one,if the final payment is increased by a balloon payment?

A loan of $10,000 is to be repaid by 60 monthly payments of $205.00 plus a smaller concluding payment made one month after the last $205 payment.Payments begin one month from now.If j₁₂ = 9%,find the amount of the smaller final payment.

Sally wants to accumulate $11,500.She makes deposits of $500 at the end of every 6 months in a fund earning interest at j₂ = 5%.It turns out that after making 18 deposits,she is still short of her goal by $306.83.What is the size of the smaller concluding deposit (drop payment)needed 6 months later in order for her to reach (or exceed)her goal of $11,500?

You can buy a used car for cash of $A on August 12,2010,OR make quarterly payments of $500,starting August 12,2010 and finishing on August 12,2016.If the loan charges interest at j₄ = 4%,what is the value of A?

A loan,A,is repaid with semi-annual payments of $1000.The first payment is due May 26,2007 and the last payment is due May 26,2012.If the interest rate on the loan is j₂ = 7% and the loan was taken out on November 26,2006,what is A?

If the accumulated value of n-payments of $250,at the time of the n^th payment,is $13,606.35,what is the accumulated value of (n-1)payments of $300,one interest period after the last payment?

You wish to have $25,000 on September 1,2012 to buy a new car.What monthly deposit is needed to achieve your goal if you can earn j₁₂ = 5.4% and you make monthly deposits from October 1,2007 to September 1,2012?

Jacques takes out a loan and agrees to pay it back with payments of $500 at the end of every 6-months for 10 years at j2 = 8% (20 payments in total).He makes the first 3 payments (time 1 to 3),but misses the next 3 (time 4 to 6).What single payment would he need to pay at the time of the 7th payment (time 7)that would make up for the 3 missed payments AND pay off the remaining payments?

Ken Tuckey takes out a loan today to be repaid with quarterly payments of $688.64 over 4 years (first payment 3 months from today).If the interest rate on the loan is j₄ = 7.2%,how much total interest does Ken pay over the life of the loan?

A university student wins a scholarship worth $50,000.Instead of the lump sum,she chooses to be paid by 48 monthly payments of $R,with the first monthly payment to be made 5 months from now.If the money earns interest at j₁₂ = 9%,what is the monthly payment?

You borrow $A on September 28,2009 at j₁₂ = 6%.You repay the loan with monthly payments of $250 starting October 28,2009 and ending on October 28,2012.What is the value of A?

You own shares in the XYZ company.For the first 10 years that you owned the shares,they paid a dividend of $150 every 6 months (paid at the end of every 6 months).However due to a downturn in the economy,no dividend has been paid in the past 2 years.If you have reinvested the dividends in a fund earning j₂ = 5%,how much do you have today?

A student wishes to accumulate $4000 by making quarterly deposits of $200 into an account,first deposit made on January 1,2011.The account earns interest at j₄ = 6%.What is the size of the final,smaller quarterly deposit (drop payment)and on what date will this final deposit be made?

Billy deposits $500 every 3-months in a fund earning interest at j₄ = 8%.After 24 deposits,the interest rate changes to j₄ = 6%.What is the accumulated value at the time of the 40^th deposit?

You deposit $300 every 3-months.Your first deposit is made November 8,2009 and your final deposit is made November 8,2017.If the deposits earn j₄ = 8%,how much do you have immediately after the deposit on November 8,2017?