# BUS130 Foundational Mathematics For Business.

## Question:

Briefly explain how compounding interest affects the effective interest rate.

Anna invests \$900 and it grows to \$1100 over 2 year. What simple interest rate does this represent?Alexander invests \$5,000 with an interest rate at 1.4% per quarter.

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How much does the investment amount after 3 years?

Sue is saving for a trip she wants to take in three years.

To save \$4,500 and earn 5.5% compounded monthly on her funds to cover her holiday expenses, how much should she invest today? Blake Ltd recently paid a cash dividend at \$2.50 per share.

How much is a Blake Ltd share worth today? If dividends grow at 5% annually and investors expect a 13% rate on Blake Ltd shares, how high would that be?

A five-year investment will yield a return of \$5250 (i.e.

For the next five year, the investment will pay a return of \$5250 semi-annually (i.e.

An investor might be willing to pay \$40,000 to make this investment. What rate of return does she earn? A morning radio show offered four alternative prizes for one competition.

If your discount rate is 6%, which prize is most valuable?

\$5,000 per year, payable in one lump sum.

\$12,000 per Year for Eight Years, with the First Payment Today.

(c. \$20,000 today, \$80,000 six-years from now.

(d) \$15,000/year for ten year, with the initial amount due at year 5.

(e). Name the most important prize.

(Give a reason why you chose this prize.

BCD Ltd issued \$1,000 par value debentures that paid 8% annually.

If you require a rate of return of 12% p.a. and the debentures mature within 7 years, how much will the debenture be worth to you?

If you take out a loan of \$460,000 over 20 years, at 5.5% interest rate, and are to repay it with equal monthly payments:

Calculate monthly repayments.

Calculate the amount that is owing after ten years.

Calculate the interest that will be paid over the loan’s life.

The current market price for a share of the company is \$28, and the next anticipated dividend is \$1.85. Expected growth in dividends at 6% p.a.

What is the expected return rate for shareholders now? Should you buy the shares of the company if your rate of return is 10%?

(i) If my maximum monthly repayments are \$250 per week, how long does it take to pay off the debt?

Comment on (i)

How much should be invested now so that a university student could withdraw \$1,500 each 6 months for 4 year?

The interest rate is 6.5% and the first amount must be withdrawn within 10 years.

Birch corporation’s \$1,000 par bonds mature in 12 year and pay 6.5% coupon interests.

The bond price is \$1,100. Your return requirement is 8%.

Calculate the expected rate of return for the bond.

Green’s preference stocks are available for \$62.50 each, and pay \$3.25 per six-month.

If these securities were purchased at their market value, what is your annual expected rate to return?

JT Ltd suspended its dividend payments due to the current global economic climate.

The dividends of \$3.75 should resume in five years, and will increase at a rate 4% per annum thereafter.

What is the current value the firm’s shares if the return requirement is 11%? A \$2,000 bond has 8 years remaining and is currently being sold for \$2255.

What is the coupon interest rate of the bond?

The firm’s return of equity is 15%. Therefore, the management plans to invest 25% of what it earns each year.

Calculate the firm’s growth rate. The company anticipates paying a \$4.50 dividend at the end of this year. The required rate of return for the firm is 14%. What is the firm’s share value?

Initial deposit of \$3,000 to a savings account. The account will pay 6% compounded every year for five years.

In 6 years, you will deposit \$500 annually for 8 years into the savings account. After that, the interest rate increases to 6.8% compounded semiannually.

What is your account balance after 13 years?

The Queen’s Ordinary Shares dividend is expected to reach \$3.90 next fiscal year.

For the next two year, this dividend is expected grow at a rate 7%.

This growth should stop at 4% after that and continue at the same rate for as long as there is no more growth.

How much is the firm’s current value if it is required to earn 12 % on these shares?

Chris Brown wants to create a permanent scholarship that pays \$5,000 an year at the start of each academic year for promising Veterinary Science students.

If interest is compounded monthly at 13%, how much would he need?

The following prizes could be substituted for a morning radio show’s competition prize.

If your discount rate is 6%, which prize is most valuable?

\$5,000 per year, in perpetuity, the first payment being made after 1 year.

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