# Interest Rate Fundamentals

- (Interest Rate Fundamentals; 10 points) You read in
*Businessweek*that a panel of economists has estimated that the long-run real growth rate of US economy over the next five-year period will average 3 percent. In addition, a bank newsletter estimates that the average annual rate of inflation during the five-year period will be about 4 percent. What nominal rate of return would you expect on US government T-bills during this period?

__SOLUTION__

Nominal rate of return

This is calculated using the following formula;

Real rate of return=3%

Expected Rate of inflation=4%

Therefore,

Calculating those in bracket;

Multiplying those in bracket we obtain;

Converting it to percentage;

**The expected nominal rate of return on the US government T-bills during the period is 7.12%**

- (Interest Rate Fundamentals; 16 points) What would your required rate of return be on common stocks if you wanted a 5 percent risk premium to own common stocks given what you know from problem #1? If common stock investors became more risk averse, what would happen to the required rate of return on common stocks? What would be the impact on stock prices?

Where is the risk premium for asset I given as 5%

is the expected return for asset i and that is what we are looking for and

is the nominal return on the free asset given as 7.12%

- (Internet Activity; Interest Rate Fundamentals; 20 points) Go to http://www.bloomberg.com/markets/rates-bonds/government-bonds/us/. Based on the most recently released daily data (i.e., the data released on the day when you work on this assignment), complete parts a and b below:
- (5 points) Bank prime loan charges 4.25% currently. Find yield for 12-month Treasury bills from the Bloomberg website and indicate the size of current default risk premiums for bank prime loans.

__SOLUTION__

- (15 points) Prepare a yield curve or term structure of interest rates based on today’s yields on U.S. Treasury securities. Briefly comment on the shape of current yield curve (i.e., is it normal or inverted? Steep or flat? What does it tell you about the current status of the US economy?)

** **

The curve presented from above is a normal curve, and this curve shows that the economy of US is currently expanding. The curve clearly shows the economy is growing and that the investors are also confident about the economic performance of the country in the future. As the curve shows, on the longer maturity bonds, investors demand more yield (additional premium), and this is brought about by the fact that money is tied up for longer periods of time. On the other hand, there is a greater demand for the short-term securities and this has pushed the yields even lower.

- (24 points) Solve the following problems using both formulas and Excel spreadsheet
- You have just made your first $2,000 contribution to your individual retirement account. Assuming you earn a 10 percent rate of return and make no additional contributions, what will your account be worth when you retire in 45 years? (5 points)

__SOLUTION__

In this problem, the investment that is made would become the present value and the rate of return would become the interest rate. If any investment is made today, then the future value would be obtained at the end of 45 years. The future value (FV) of the retirement account is then calculated as follows;

Where

Calculating this by inserting values, we obtain;

**Therefore, the Future Value (FV) after 45 years is **

- You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100
^{th}birthday (assuming you’re around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 10 percent? (5 points)

__SOLUTION__

From the formula above, Present value (PV) can easily be calculated as;

Rearranging this formula;

The Future Value give in the question is

Interest, is given as

And the time given by n is 80 years. Replacing them in the equation above;

**Hence the present value is **

- Assume the total cost of a college education will be $250,000 when your child enters college in 18 years. You presently have $43,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education? (5 points)

__SOLUTION__

In this problem, we are given the present value, time/ duration and the future value. We then need to calculate the interest rate. This can be calculated using the following formula;

Putting the values,

Calculating the values on the left side;

Making the value of I the subject of the formula,

**Hence the interest rate is **** converting it to percentage, we get**

**Interest rate=10.2743%**

- You’re trying to save to buy a new $150,000 Ferrari. You have $40,000 today that can be invested at your bank. The bank pays 5.5 percent annual interest on its accounts. How long will it be before you have enough to buy the car? (5 points)

__SOLUTION__

This questions requires calculation of time, given in the formula as n. in order to calculate this, we use the following formula;

Rearranging the formula,

Taking logarithm on both sides;

Making n (time) the subject of the formula

Given FV=$150000

PV=40000

I=5.5%=0.055

Replacing the value on the equation;

Therefore, n= 24.693 years

**Hence the time taken is 24.693 years.**