Exam 9: Compound Interest: Further Topics and Applications

An $8600 investment was worth only $7900 one year later. If the rate of total return for the year was -5%, how much income was received from the investment during the year?

What is the effective rate of interest corresponding to a nominal rate of: a) 8% compounded semiannually? b) 12% compounded quarterly?

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

If a company's annual sales grew from $165,000 to $485,000 in a period of eight years, what has been the compound annual rate of growth of sales during the period?

A 30-year, $1,000 strip bond was traded for $167, four years after it was issued. What was the semi-annually compounded nominal rate at that time?

Determine how long will take to triple money given an interest rate of 4.39% compounded monthly. Calculate to the nearest day.

What is the effective interest rate corresponding to a nominal annual rate of: a) 9% compounded semiannually? b) 9% compounded monthly?

What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months?

An invoice indicates that interest at the rate of 1.75% per month will be charged on overdue amounts. What effective rate of interest is being charged?

Columbia Trust wants its annually, semiannually, and monthly compounded five-year GICs all to have an effective interest rate of 3.75%. What nominal annual rates should it quote for the three compounding options?

An investor's portfolio increased in value from $35,645 to $54,230 over a six-year period. At the same time, the Consumer Price Index rose by 26.5%. What was the portfolio's annually compounded real rate of return?

Jeff purchased some Mitel preferred shares on the Toronto Stock Exchange for $13.50. The shares pay a quarterly dividend of $0.50. Nine months later the shares were trading at $15.25. What was Jeff's rate of total return for the 9-month period?

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?

A stock valued at $75 decreased by 20% and then increased by 20%. What was the value of the stock after the increase?

A trust company pays 3.5% compounded semiannually on its three-year GICs. For you to prefer an annually compounded GIC of the same maturity, what value must its nominal interest rate exceed?

Rounded to the nearest month, calculate how long it will take money to lose half its purchasing power to a 3.25% inflation rate.

If a series of compound percent changes are all negative, is the overall percent decrease larger or smaller (in magnitude) than the sum of the individual changes? Justify your answer.

If money is worth 8% compounded quarterly, how long (to the nearest day) before a scheduled payment of $6,000 is $5,000 an equivalent payment? For the purpose of determining the number of days in a partial calendar quarter, assume that a full quarter has 91 days.

Suppose the periodic rate for one month is 0.5%. Is the equivalent periodic rate for six months (pick one): (i) equal to 6(0.5%) = 3%? (ii) less than 3%? (iii) greater than 3%? Answer the question without doing calculations. Explain your choice.

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