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FINM7006: Applied Foundations of Finance

Financial Mathematics: Solutions to Practice Questions

Question One

A woman invests $1,000 at 10% p.a compounded annually and plans to hold this investment for five years. How much will she have at the end of her holding period?

The value of the woman’s investment at the end of her holding period is calculated as:

Question Two

If you wish to provide $20,000 for your newborn’s University education, how much should you invest now, given the interest rate that will accrue on the investment is 10% p.a. compounded monthly?

In order to determine how much you should invest now, calculate the present value of $20,000 received 18 years from now, bearing in mind that interest is compounded monthly.

Question Three

A company needs $10,000 in 5 years to replace a piece of equipment. How much must be invested now at an interest rate of 8% p.a. compounded daily in order to provide for this replacement?

To determine the amount the company must invest now, simply calculate the present value of $10,000 paid in 5 years, bearing in mind that the interest rate is compounded daily.

Question Four

A company needs $10,000 in 5 years to replace a piece of equipment. How much must be invested each year at 8% p.a. compounded semi-annually in order to provide for this replacement?

To determine the amount the company must invest annually, simply use the future value of an annuity formula, bearing in mind that the interest rate is compounded semi-annually.  Therefore, as investments will be made on an annual basis, we must calculate an annual effective interest rate to use in the annuity calculation.

Question Five

A woman wants to provide a $3,000 university scholarship every year for ten years. The first scholarship is to be awarded one year from now. If the university can earn a 4% p.a. compounded monthly as a return on their investments, how much should the woman give now?

To determine the amount the woman must invest now, simply use the present value of an ordinary annuity formula, bearing in mind that the interest rate is compounded monthly.  

Question Six

Annual sales revenue for your division was $2 million last year.  Further, you expect that these revenues will grow indefinitely at a rate of 10% p.a. What is the present value of sales if the appropriate interest rate is 12% p.a. compounded annually?

To calculate the present value of sales, simply use the formula for a perpetuity with constant growth: