Exam 9: Compound Interest: Further Topics and Applications

The following table presents the rates of total return in successive years from 2008 to 2012 for the Ethical Growth Fund and for the benchmark Toronto Stock Exchange S&P/TSX Composite Index. By how much did the mutual fund's overall percentage return exceed or fall short of the Index's growth?

At the end of 2009, the Industrial Alliance (IA) Group Dividends Fund had the best 10-year compound annual return of any Canadian diversified equity mutual fund. During the 10-year period, this fund invested primarily in the shares of large Canadian companies. The fund's annual returns in successive years from 2000 to 2009 inclusive were 33.5%, 9.2%, 2.2%, 25.8%, 17.9%, 27.9%, 19.7%, 6.3%, -26.0%, and 21.5%, respectively. For 3-year, 5-year, and 10-year periods ended December 31, 2009, what was the fund's equivalent annual compounded return?

Calculate the missing interest rate (to the nearest 0.01%)

A few years ago, Larissa invested $1500 at 3.75% compounded quarterly. If the investment is worth $1693.46 today, how many years ago did Larissa make the investment?

If the S&P/TSX Composite Index declined from 14,614 to 14,238 over a 50-day period, what were the simple and effective annualized rates of decline in the index during the period?

Adjusted for stock splits, the price of Microsoft shares rose 88.3%, 56.4%, 114.6%, and 68.4% in the years 1996 to 1999 respectively. In 2000, the share prices fell 62.8%. a) What was the overall five-year percent change in the price of Microsoft shares? b) If the share price at the end of 2000 was $43.38, what was the price at the beginning of 1996?

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's total return?

What monthly compounded interest rate is equivalent to 6% compounded: a. annually? b. semiannually? c. 6% compounded quarterly?

If an interest rate of 8.9% compounded semiannually is charged on a car loan, what effective rate of interest should be disclosed to the borrower?

A furniture company has decided to drop the effective rate on its credit card by 2%. The store currently charges a periodic rate of 1.85% per month. What new periodic rate should the store advertise?

Kristina was earning $10.00 an hour four years ago. Today, she earns $13.50 an hour. At what equivalent compound annual rate has her salary grown over the four years?

A $9,000 payment on March 1 was not paid. Instead $9,140.65 was paid earning 6.3% interest compounded semi-annually. The payment was made on July 1.

If the Consumer Price Index rose from 109.6 to 133.8 over an 8½-year period, what was the equivalent compound annual inflation rate during the period?

What was the annually compounded nominal rate of growth if the future value of $1,000 after 20 years was $2321.06?

Jerome is planning on contributing $5,000 at the end of each semi-annual period for 8 years in an investment providing 8.4% compounded quarterly. At the end of this time, Jerome plans to reinvest this amount in another investment that will provide him with the opportunity to withdraw $1,500 per month over 5 years and have $10,000 remaining. Based on monthly compounding, determine what the rate of interest that will achieve this goal.

A bank pays a simple interest rate of 2.1% on 30 to 179-day GICs of at least $100,000. What is the effective annualized rate of return: a) On a 40-day GIC? b) On a 160-day GIC?

If the population of Green City is growing at a rate of 5% per year, how long will it take to grow from 2,300 to 10,000?

Wilf paid $557.05 for a $1,000 face value strip bond. At this price the investment will yield a return of 5.22% compounded semiannually. How long (to the nearest day) before its maturity date did Wilf purchase the bond? Assume that each half-year has exactly 182 days.

An investment earned 6.3% compounded annually for two years, 5.4% compounded semi-annually over another 2 years, and 4.5% compounded quarterly over the last 6 years. Determine the average annual rate of return over this 10 year period based on monthly compounding.

If the Halifax Real Estate Board reports that house prices increased by 8% during the first seven months of the year, and if prices continue to rise at the same rate for the subsequent five months, what will be the (compound) increase for the entire year?