# Business Calculus : Time Value of Money

There are 3 sheets in the file with approx 21 questions. Most of them are mathematical, but there are also some that are subjective type questions.

I have also attached the tutorials with the problem sets in the same file.

In the problem sets on sheet one, I will answer number 9.

Chapter 3: Project 3 Mortgages: Principal and Interest

This project is based on Group Activity 2 at the end of chapter 3.

A computer technician receives annual bonuses for 4 years, which are listed in

Table 1.

Year Bonus

1 $2,500

2 $6,500

3 $4,000

4 $7,500

Each time he gets a bonus, he immediately invests it in a mutual fund. From

year to year, the interest varies on this fund.

One year after making the last investment, the salesman closes out the fund

and receives a payment of $40,000. He would like to find a compound interest

rate that represents the interest his investments earned over the entire 4 year

period. This rate is known as the yield to maturity.

If r is the yield to maturity, then the compound interest formula expresses the

value of each investment at the end of the 4th year in terms of r.

1. What would the formula for the value of the first investment (year 1) be

at the end of the 4th year? (Hint: use the compound interest formula as discussed

in Section 2.2).

2. Repeat part (1) for the investments in the second, third, and fourth year.

3. If you add all your answers from parts (1) - (2), you will have a function of r,

which is the yield to maturity. What should this function equal?

4. Your function in part (3) should be equal to $40,000. Why?

Using Goal seek, find an appropriate value of r.

5. Fill in the following table for r, f(r), g(r), where r ranges from -7 to 7,

f(r) = 40,000, and g(r) is your function from part (3).

r f(r) g(r)

-7 $40,000

6. Using the table above, graph the function with makeplot. Graphically

estimate a value for r.

7. How do your answers from (4) and (6) compare?

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