Chapter 3 and 4 Review

^[1] Sam agrees to make a payment of $1,000.00 in 3 months at 8% simple interest. How much money is Sam borrowing today?

^[2] Alixe borrowed $5,000 today at 12% simple interest. How much will she owe the bank when she pays off the debt in 180 days?

^[3] Myrna borrowed $5,000 from the bank some time ago at 9% simple interest. She paid off the loan today with one payment of $5,675 . How many months ago did she borrow the $5,000? (Hint: it’s easier to use I = Prt.)

^[4] You would like to save to purchase a Kia automobile. You deposit $3,500 into a GIC that pays 8% interest, compounded quarterly. You need to save at least $5,000 to buy the car. If you make no more contributions, how many years will it take you to reach your goal?

^[5] Lindsay made an investment of $1,500.00 made 42 months ago. It is now worth $2,110.65. What nominal rate of interest, compounded semi-annually, did this investment earn?

^[6]  Answer the following

1. What nominal rate, compounded semi-annually, is equivalent to 9% compounded quarterly?
2. What nominal rate, compounded monthly, is equivalent to 9% compounded quarterly?
3. What nominal rate, compounded quarterly, is equivalent to 12% compounded annually?

^[7] A debt of $6,000 due today and $8,000 due 2.5 years from today is to be paid off with two payments. The first payment is to be made six months from today, and a second payment, $5,000 larger than the first, 15 months from today. What should the two payments be if money is worth 9%, compounded quarterly? Use 15 months as the focal date.

^[8] Pavel was supposed to pay $10,000 today. Instead, he arranged with the bank to pay $3,000 12 months from today, followed by two equal payments in 18 months and in 30 months from today. The interest rate is 8% compounded quarterly. Calculate the size of each payment? Use 30 months as the focal date.

^[9] Anna borrowed $3,000 from her line of credit 8 months ago and a further $5,000 3 months ago . She arranged with the bank to pay off the line of credit with two payments. The first payment, 6 months from today, will be twice as large as the second payment made one year from today. The bank charges you 9% interest, compounded monthly. Use 6 months as the focal date.

1. Find the size of each payment.
2. How much interest will she pay?

^[10] A debt of $15,000 is due today. Instead, the borrower agrees to make one payment of $5,000 in 6 months and 2 equal payments in 3 months and 12 months from today, with simple interest charged at 6%. What is the size of each payment? Use 6 months as the focal date.

^[11] Matt is going to purchase a car and is given two options to pay.

• He can pay $25,000 in cash today, or
• $12,000 after one year, and a second payment of $15,000 after 18 months.

Which option is better? Your answer should be stated in terms of today’s dollars. The interest rate is 7% compounded semi­ annually?

^[12] Mortel Inc. borrows some money today. In 10 months it must pay back $854,962.11. How much did Mortel borrow today if it is being charged 8% interest, compounded monthly?

^[13] An investment of $5,000 made 27 months ago is now worth $7,756.64. What nominal rate of interest, compounded quarterly, did the investment earn?

^[14] Julia is seeking an investment and has narrowed her search to three different funds.

Fund A offers a return of 12.2% compounded quarterly.

• Fund B offers a rate of 12.4% compounded semi- annually.
• Fund Coffers a rate of 12% compounded monthly.

Convert all rates to effective rates and explain which rate is the best investment.

^[15].      Serena invests $3,000 in a bond fund today. Her investment earns 4% compounded semi-annually in the first year, 6% compounded quarterly in the second year and 8% compounded annually in the third year.

1. How much would the $3,000 investment be worth at the end of the third year?
2. If, in the fourth year the bond fund loses money and the value of her investment falls by $200, what average annual rate of return, compounded quarterly, did she earn for the four years that she held the investment?
3. A friend has invested in a different bond fund and says she tripled her money in eight years. What nominal rate of interest, compounded semi-annually, did she earn?
4. At 9% compounded quarterly, how long would it take you to triple your money?

^[16] Mike purchased a two-year term deposit that pays interest at 5.7% compounded quarterly. At the end of the two years he renews the term deposit plus accumulated interest at 6.2% compounded semi-annually for an additional three years. At the end of the five years he has $6,724.84? How much did Mike initially pay for the term deposit?

^[17] Yolanda has a debt that comes due on November 26th and another that comes due on April 6th of the following year. She would like to celebrate Valentines Day by paying off the debts with a single payment on February 14th. How much should she pay if interest is 5% simple and each debt was for $1,000? (Use February 14th as the focal date.)

^[18] Davis borrowed $5,000, and 18 months later repaid the loan with a single payment of $5,600. Calculate the simple interest rate.

^[19] Your investment of $8,500 grew to $8,893.09 at an interest rate of 4% simple. How many days was it invested?

^[20] How much money do you need to deposit to earn $850 in interest in 18 months with interest at 6% compounded quarterly?