^[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 semiannually.
• 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.

(a) How much would the $3,000 investment be worth at the end of the third year?

(b) 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?

(c) A friend has invested in a different bond fund and says she tripled her money in eight years. What nominal rate of interest, compounded semiannually, did she earn?

(d) 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 Valentine’s 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?

 

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