Chapter 5 Review

^[1] What will be the amount in an RRSP at the end of 20 years if monthly contributions of $500 are made at the end of each month and the RRSP earns 6% compounded monthly for the first 15 years and 7.5% compounded monthly for the remaining 5 years?

^[2] You have $4,000 in your savings account today. You will deposit $500 per month starting one month from now.

1. How much will you have in your savings account at the end of 5 years if you earn 6% compounded monthly?
2. How much interest would you earn?

^[3] You have just purchased a preferred share for $50.00. The company pays a dividend of $1.00 every quarter. One year later, when you sell the share, the interest rate is 10% compounded quarterly. How much will you gain or lose? (The next dividend is due in three months.)

^[4] You purchase a car and finance $10,000. The loan is to be repaid with monthly payments of $200 made at the end of the month for 5 years. What effective rate of interest is being charged?

^[5].       You begin a savings plan. Starting now and for ten years, you deposit $100 per month into an account that pays  = 6%. After 10 years, how much interest will you have earned?

^[6].      Upon graduation, you have a student loan of $15,000. The most you can afford to pay is $550 per month. How long will it take you to repay the loan with payments of $550 per month starting in one month if the interest rate is 6% compounded monthly?

^[7] You purchase a car for $25,000 and make a 20% down payment. Interest is charged at 6% compounded monthly, and you will make 6 years of monthly payments. Find the size of the monthly payment if your first payment is in one month. (Round payment up to next cent.)

^[8] You have decided to take a passive approach to fitness and order the ‘Ab-Cruncher’ from the shopping network. The Ab-Cruncher can be purchased for four easy monthly payments of $19.95 starting in one month. If interest is charged at 112 = 12%, find the cost of financing.

^[9] You are 25-years-old and want to retire when you turn 55. Starting today you will deposit $200 into an RRSP every month for 30 years. You will then use the accumulated funds to purchase a 10-year annuity with the first withdrawal one month after your 55th birthday. Assume that the RRSP and the funds invested in the annuity earns 6% compounded monthly.

1. Find the size of the monthly withdrawals.
2. You decide that you will need $3,000 per month to live on when you retire at age 55. How much extra money must you contribute to your RRSP every month, so you can withdraw $3,000 every month for 10 years?

^[10] You contribute $2,500 into your RRSP at the end of every quarter for 5 years. If your RRSP earns 8% compounded quarterly, how much interest will you earn in the 5 years?

^[11] You borrow $50,000 and agree to make monthly payments for 15 years with the first payment one month from now. Calculate the size of your monthly payments if the interest rate is 9% effective.

^[12]  Paula, a BCIT business student, borrowed $5,000 from her parents to cover expenses and agreed to repay the debt with 20 equal monthly payments with the first payment due in 2 years. The interest rate is 12% compounded monthly.

1. How large is each payment?
2. How much interest did Paula pay her parents?

^[13] Barton Fink bought a second hand car with $1,000 down and signed a contract agreeing to pay $299 every month for 3 years at 9% compounded monthly. The first payment is made one month later.

1. What is the cash price of the car?
2. How much interest will Barton have paid over the 3 years?

^[14] A debt of $5,000 is to be paid off by making payments of $502.31 at the end of every 3 months. If interest is 12% compounded quarterly, how long will it take to pay off this debt?

^[15] You need to set aside $2,500 for your vacation in Moose Jaw to celebrate graduation from BCIT 21 months from today. If your bank pays 9% compounded quarterly, how much must you deposit into your account at the end of every quarter to have $2,500 in 21 months?

^[16] A home entertainment centre may be purchased for $2,299 or by making payments of $199 to be made at the end of every month for 12 months.

1. What nominal rate of interest, compounded monthly, is being charged?
2. What is the effective rate of interest rate charged?

^[17] Fred Rock will deposit $500 in his RRSP every month for 15 years starting today. One month after the last deposit, he will withdraw the money in equal monthly withdrawal for 10 years.

1. Find the size of the monthly withdrawals if the invested funds earn 7.0% compounded monthly.
2. How much interest will Fred earn over the 25 years?

^[18] Sam Shepherd wants to borrow some money from the Federal Business Development Bank to open a doggy daycare business. The terms of the loan specify that no payments are required in the first year of the business. Starting in the second year, payments of $1,000 at the end of every three months are required for a period of five years (i.e., until the end of the sixth year of the business). If interest is 8% compounded quarterly, how much money is he borrowing?

^[19] Sam N Ella has just turned 50 years old today. He has decided to start saving for his retirement. He plans to retire when he turns 65. He will set aside $1,500 per quarter, starting today, into a money market account that earns 4% compounded monthly.

1. How much will Sam have on the day he retires?
2. How much interest will he have earned?

^[20] Judith Fortune recently won $500,000 from a hospital lottery. She has decided to put some of her winnings into an RRSP. Miss Fortune is 55 years old and plans to retire at age 65. She would like to receive $2,000 per month for twenty years starting on her 65th birthday.

1. If she can earn 6%, compounded monthly, how much of her winnings should she put into her RRSP today?
2. Miss Fortune has changed her mind and has decided to put half of her winnings into an RRSP instead. How much extra will she receive per month when she retires?

^[21]A dining room suite sells for $4,999. It may be purchased from Junk-O Furniture by making a down payment, followed by monthly payments of $245 for a year-and-half. (The first payment is one month later.) Interest is j₁₂ = 12%. Find the size of the down payment.

^[22]An alumnus wants to donate a sum of money to his Alma Mater that will provide a scholarship of $750.00 every 6 months in perpetuity. If money can be invested at 6% compounded semi-annually and the first $750.00 is to be awarded at the end of six months how much must he donate to the school today?

^[23] You have decided to purchase preferred shares of No-Vision Eye Treatment Centre that pays a semi-annual dividend of $1.75 per share. Current interest rates are 7% compounded semi-annually and the next dividend is due in six months.

1. What should you be willing to pay per share?
2. Two years later the interest rates drop to 5% compounded semi-annually. You have decided to sell your shares. Calculate your gain or loss per share if the next dividend is due in six months – and the dividend per share remains the same.

^[24] You purchase 250 preferred shares of Silent Witness Security Systems Inc. that pays a dividend of $2.25 per share every 3 months. Current interest rates j₄ = 6%.

1. What would you be willing to pay for the 250 shares?
2. If interest rates rise to 8% compounded quarterly, how much would you expect to gain or lose if you sell all of your shares? Note: the next dividend is due in 3 months and the dividend per share is still $2.25.