Exam 9: Compound Interest: Further Topics and Applications

The average Canadian home was $70,000 in the early 80s. In 30 years, the average increased to $390,000. The average increase is 5.89%

A T-bill with 125 days remaining to maturity is discounted to yield 4.6% pa simple interest. What is the effective annualized rate of return on the T-bill?

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

Calculate the effective annual rate, if $100 grew to $165 in 11.5 years with quarterly compounding.

What is the quarterly compounded nominal rate that is equivalent to 18% compounded monthly?

Rose purchased units of the Trimark Fund 1 year ago at $24.10 per unit. Today they are valued at $25.50. On the intervening December 31, there was a distribution of $0.83 per unit. ("Distribution" is the term used by most mutual funds for income paid to unit holders.) Calculate Rose's income yield, capital gain yield, and rate of total return for the year.

A bank pays a simple interest rate of 8% per annum on 40-day GICs. What is the annualized rate of return?

If the number of workers in the forest industry in Canada declined by 41% from the end of 1993 to the beginning of 2009, what was the compound annual rate of attrition in the industry?

How long will it take a $2,000 investment to grow to $2501.50 if it earns 4.5% compounded quarterly?

Calculate the term of the loan or investment:

Can the income yield from an investment be negative? Explain or give an example.

The current (simple annualized) yield, based on the holding-period return for the most recent 7 days, is reported for a money market mutual fund as 6.17%. What is the fund's corresponding effective (annualized) yield?

Martha is planning her retirement in 10 years' time. She contributes a lump sum deposit of $10,000 now in a plan earning 5.4% compounded semi-annually. Two years later, she will deposit $20,000 in another investment earning 4.8% compounded monthly. In the final 5 years, she plans on contributing $1,000 per month. Based on quarterly compounding, determine what the rate of interest will be on the final investment if she wishes to end up with $112,000.

From a lender's point of view, would you rather disclose to borrowers the nominal interest rate or the effective interest rate?

Terry was supposed to pay $800 to Becky on March 1. At a later date, Terry paid Becky an equivalent payment in the amount of $895.67. If they provided for a time value of money of 8% compounded monthly, when did Terry make the payment?

What is the semi-annually compounded nominal rate that is equivalent to 10.5% compounded monthly?

At 14% compounded annually, an investment of $50,000 will grow to $1,000,000 in 22.86 years. How much longer will it take at 11% compounded annually?

The current balance on a loan is $3319.59. If the interest rate on the loan is 5% compounded monthly, how long ago was the $2,870 loan made?

ABC Ltd. reports that its sales are growing at the rate of 1.3% per month. DEF Inc. reports sales increasing by 4% each quarter. What is each company's effective annual rate of sales growth?

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