Exam 9: Compound Interest: Further Topics and Applications

What rate of return in the second year of an investment is required to break even after a 30% loss in the first year?

To the nearest month, how long will it take an investment to double in value if it earns 7.5% compounded semiannually?

The Wilsons bought their home 16 years ago for $128,000. Its value now is $141,000. At what annual rate has the value of their home appreciated since they bought it?

$7,500 was borrowed for a four-year term at 9% compounded quarterly. The terms of the loan allow prepayment of the loan based on discounting the loan's maturity value at 7% compounded quarterly. How long (to the nearest day) before the maturity date was the loan prepaid if the payout amount was $9,380.24? For the purpose of determining the number of days in a partial calendar quarter, assume that a full quarter has 91 days.

Rounded to the nearest month, how long before a scheduled payment of $10,000 would a payment of $5,000 be an economically equivalent alternative? Assume money is worth 5% compounded annually.

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

How long did it take $4,625 earning 4.875% compounded annually to grow to $6768.42?

Calculate the term of the loan or investment:

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 income yield?

Manuel begins investing $700 per month for 4 years in an account earning 3.8% compounded annually. At the end of this time, he makes a $20,000 lump sum deposit on top of the accumulated investment into another account. At the end of 5 years, this amount has accumulated to $84,000. Based on monthly compounding, determine what the rate of interest that will achieve this goal.

Determine the annual nominal rate of a credit card charging 2.3% effective rate based on monthly compounding.

15 years ago, Alyssa made an initial deposit of $5,000 along with quarterly contributions in an investment earning 6.1% compounded monthly. 10 years ago, she deposited another lump sum of $25,000 in another investment. If her cumulative investments were $100,000 at the end of the 15 years, determine the rate of interest earned on the second investment based on annual compounding.

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

What rate of interest compounded quarterly has an effective rate of 6%?

At the end of 2012, the Trans IMS Canadian Growth Fund had one of the worst 10-year compound annual returns of any Canadian diversified equity mutual fund. The fund's annual returns in successive years from 2000 to 2009 inclusive were -12.8%, -38.3%, -24.1%, 25.4%, 9.2%, 18.6%, 12.0%, -0.2%, -38.5%, and 15.6%, respectively. For 3-year, 5-year, and 10-year periods ended December 31, 2012, what was the fund's equivalent annually compounded return?

Monty purchased a strip bond for his RRSP. He paid $3,800 for a $5,000 face value bond with three years remaining until maturity. What semiannually compounded rate of return will he realize over the three years?

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 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?

Maury invested $5,000 in a selection of high-tech stocks. After six years of careful trading, his investments were worth $79,700. At what quarterly compounded nominal rate did his investments grow?

An effective rate of 6.6% (based on quarterly compounding) has a higher nominal rate than an effective rate of 6.5% (based on monthly compounding).