Exam 8: Compound Interest: Future Value and Present Value

Commercial Finance Co. buys conditional sale contracts from furniture retailers at discounts that provide a 12% compounded monthly rate of return on the purchase price. What total price should Commercial Finance pay for the following three contracts: $950 due in 4 months, $780 due in 6 months, and $1,270 due in 5 months?

Calculate the combined equivalent value of the scheduled payments on the indicated dates. The rate of return that money can earn is given in the fourth column. Assume that payments due in the past have not yet been made.

How much more will an investment of $10,000 earning 8% compounded annually be worth after 25 years than after 20 years? Calculate the difference in dollars and as a percentage of the smaller maturity value.

What total interest will be earned by $5,000 invested at 5.4% compounded monthly for 3½ years?

If the current discount rate on 15-year strip bonds is 4.75% compounded semi-annually, how many $1,000 face value strips can be purchased with $10,000?

What periodic payment will an investor receive from a six-year, $90,000 monthly payment GIC earning a nominal rate of 4.2% compounded monthly?

Jorge is unable to make a $4,500 payment due today. He proposes to settle the obligation by making three equal payments-one today, another in four months, and a third in nine months. What must each payment be to make the proposed payment stream equivalent to the scheduled payment if money can earn 7.2% compounded monthly?

A $15,000 loan at 5.5% compounded semi-annually is advanced today. Two payments of $4,000 are to be made 1 year and 3 years from now. The balance is to be paid in 5 years. What will the third payment be?

Fred borrowed money 18 months ago at 12% compounded semi-annually. He now owes a total of $5,450. How much of this is interest?

Suppose an individual invests $1,000 at the beginning of each year for the next 30 years. Thirty years from now, how much more will the first $1,000 investment be worth than the 16^th $1,000 investment if both earn 8.5% compounded annually?

If your client's objective is to have $10,000 in four years, how much should he invest today in a product earning 5.5% compounded annually? (Taken from CIFP course materials)

Joe Superstar has just signed a "four-year, $68-million deal" with the Toronto Blue Jays. The terms of the contract include a signing bonus of $4.8 million and salaries of $10 million, $17.2 million, $17.5 million, and $18.5 million in successive years of the contract. The news media always ignore the time value of money when they report the "value" of professional athletes' contracts. What is the economic value of Joe's contract on the date it was signed? Assume that the signing bonus was paid on that date, that the annual salaries will be paid in lump amounts ½ year, 1 ½ years, 2 1/2 years, and 3 ½ years later, and that money is worth 5% compounded semi-annually. Round the answer to the nearest $1,000.

Patrice defaulted on payments of $1,000 due one year ago and $1,500 due six months ago. A Small Claims Court orders her to make three payments-$800 one month from now, $900 four months from now, and a third payment seven months from now. The third payment is to be determined so that the creditor will end up in the same economic position as if the original payments had been made on time. The court set the fair rate of return at 4.2% compounded monthly. What should the third payment be?

A 25-year, $10,000 strip bond was issued at a market rate of 9.4% compounded semi-annually. What was the issue price?

Two payments of $2,000 each are scheduled for six months from now and two years from now. They are to be re-scheduled as follows: a payment one year from now and a second payment, half the size of the first payment, three years from now. What must the amount of each payment be for the replacement stream to be equivalent to the originally scheduled stream? Assume that money can earn 7.8% compounded semi-annually.

A $7,500 loan at 9% compounded monthly requires three payments at 5-month intervals after the date of the loan. The second payment is to be twice the size of the first payment, and the third payment is to be double the amount of the second payment. Calculate the size of the second payment.

How much more will an investment of $10,000 be worth after 25 years if it earns 5% compounded annually instead of 4% compounded annually? Calculate the difference in dollars and as a percentage of the smaller maturity value.

Calculate the maturity value of the five-year compound-interest GIC whose interest rate for each year is given. Also calculate the dollar amount of interest earned in the fourth year.

Payments of $2,400, $1,200, and $3,000 were originally scheduled to be paid 1½ years ago, today, and 15 months from today, respectively. Using 6% compounded quarterly as the rate of return money can earn, what payment six months from now would be equivalent to the three scheduled payments?

For the five-year period ended December 31, 2006, the Sprott Canadian Equity Fund had the best performance of all diversified Canadian equity funds. It effectively earned a compound annual return of 31.6% compared to the average of 10.1% for over 300 diversified Canadian equity funds with a five-year history. How much more would an initial $1,000 investment in the Sprott Canadian Equity Fund have earned over the five-year period than a $1,000 investment in a fund earning the average rate of return?