Question

6. You have just sold your house for $1,000,000 in cash. Your mortgage was originally a​ 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly​ 18½ years​ old, and you have just made a payment. If the interest rate on the mortgage is 5.25% ​(APR), how much cash will you have from the sale once you pay off the​ mortgage? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

7. If the rate of inflation is 4.8%​, what nominal interest rate is necessary for you to earn a 3.3% real interest rate on your​ investment? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

8. Use the table for the​ question(s) below.

Suppose the term structure of interest rates is shown​ below:

Term	1 year	2 years	3 years	5 years	10 years	20 years
Rate​ (EAR%)	​5.00%	​4.80%	​4.60%	​4.50%	​4.25%	​4.15%

What is the shape of the yield curve and what expectations are investors likely to have about future interest​ rates?

A.​inverted; lower

B.normal; higher

C.inverted; higher

D.​normal; lower

9. In​ 2007, interest rates were about​ 4.5% and inflation was about​ 2.8%. What was the real interest rate in

​2007?

A.​1.61%

B.​1.58%

C.​1.62%

D.​1.65%

10. You are thinking about investing $5,000 in your​ friend's landscaping business. Even though you know the investment is risky and you​ can't be​ sure, you expect your investment to be worth $5,750 next year. You notice that the rate for​ one-year Treasury bills is1 %. However, you feel that other investments of equal risk to your​friend's landscape business offer an expected return of 10%for the year. What should you​ do?

Answer 1

Q6) Step 1 calculate the per month payment

Using financial calculator to calculate per month payment

Inputs: PV = -800,000

i (interest rate) = 5.25% / 12 = 0.4375%

N= 30 × 12 = 360

Fv= 0

Pmt= compute

We get, pmt as $4,417.6296

Step 2:- Now calculate the present value of the payment left to be made

Using financial calculator to calculate the present value

Inputs: N= 11.5 ×12 = 138

I/y = 5.25% / 12 = 0.4375%

Pmt= 4,417.6296

Fv= 0

Pv= compute

We get, the present value of the leftover payment to be made $456,931.4097

Cash left = 1,000,000 - 456,931.41

= $543,068.59

Q7) Nominal interest rate = [(1+real rate ) + (1+inflation rate) ] - 1

= [(1.033) (1.048)] - 1

= 1.0826 - 1

= 0.0826 or 8.26%

Q8) A) inverted, lower

Explanation: As the yield is higher in short term and lowee in long term, it means that the yield curve is inverted. If the yield keeps on decreasing, the price of the bond in future will increase and the expected interest rates will decrease or will be lower in future.

Q9) D) 1.65%

Explanation:

Real interest rate = (1+nominal interest rate)/(1+inflation rate) -1

= 1.045/1.028 - 1

= 1.0165 - 1

= 1.65%

10) Npv = - initial investment + Cash flow /(1+r)^n

= -5,000 + 5,750(1+r)^1

We use 10% interest rate because other investment has equal risk.

= -5,000 + 5,750 / 1.10

= -5,000 + 5,227.27

= $227.27

As the Npv is positive, we should accept it.