Question

Principles of Finance (FINC 311)

Homework Assignment 2

Learning Goal 1: Analytical - Apply appropriate problem-solving methodologies to the analysis and solution of financial problems

Students are able to use TVM techniques to problems involving loan payments and asset values

Student computes present and future values

1.          

                a.             You deposit $100 into an account earning a 10% annual rate of interest. How much money will you have in the account at the end of five years?

                b.             You have just won the lottery and have a choice of receiving a lump sum of $1,000,000 or an annuity of $100,000 per year for 15 years. If the appropriate discount rate is 8%, which alternative would you choose? (10 points) Explain.

                c.             What happens to the future value of a sum of money deposited for N years as the rate of return k increases? (15 points) What happens to the present value of a sum of money to be received at the end of N years as k increases?

2.             Applies TVM techniques using multiple compounding periods per year.

                a.             You are saving for retirement and have the opportunity to invest in a security that pays a 12% annual rate of return, compounded quarterly. If you invest $100,000 in the security now how much will you have in your retirement account at the end of 10 years?

                b.             Would it be better for your retirement account if the returns on the security were simply compounded once a year? (5 points) Explain why or why not. (15 points) Is more frequent compounding good for borrowers or for lenders and why? (30 points)

                c.             Colin’s grandparents want to make a gift of $50,000 towards his college education fund in 12 years. How much money would they have to deposit today in an account that accrues interest monthly if the rate quoted by the bank is 6 percent?

3.             Applies TVM techniques to real problems

                                Peter is considering making a loan of $500,000 to Paul. It is a three-year loan with annual payments due at the end of each year and a 7% annual interest rate. Find the payments that would be required to amortize the loan over the three-year period and then prepare an amortization schedule to demonstrate how the loan will be fully paid off in three years.

Year        Beginning Balance              

Payment

Interest Paid        

Principal Paid        Ending Balance

1              $500,000.00                                                        

2                                                                             

3                                                                             

Answer 1

TMV time value of money means the value of some amount today is more than the value of the same amount in future

1)

a) invested amount 100usd and the interest rate is 10%

To calculate the amount at the end of 5 years we can multiply the deposited amount with future value interest factor for 5years at10%( using future value interest factor table )

100*1.611= 161.1

1.611- future value of a rupee at 10% after 5years. Or can call as future value interest factor.

b) we should compare $1000000 with the present value of future inflows to choose an option among the 2

Present value of the amount which is same and receiving at regular and same interval can be calculate by multiplying that recurring amount with present value interest factor annuity

So pv = 100000*present value interest factor annuity at 8%for 15years from present value interest factor annuity table

100000*8.559 = 855900$

Which is less than 1000000$ so receiving 1000000 $ now is beneficial than receiving 100000 for 15 years

c ) future value of the sum increases with increase in rate k when the time n is fixed

FV = 1*(1+k) for 1 year so directly proportional

And the present value will decrease when the rate k is increase and time n is fixed , the value decrease as the required rate increase

Pv= 1/(1+k)

It means pv and k are indirectly proportional

2)

a) time 10 years and compounded quarterly means time periods 10*4 =40

Interest is 12/4=3 percent per quarter

In the question they asked how much will you receive in future means we have to calculate future value of 10000$ at 3% for 40 periods

100000* FVIF for 40 periods and at 3%

100000*3.262= 326200$

We can get 3.262 with calculator also

So we can have 326200$ at the end of 10years

b)

Compounding means frequency of adding interest to principal amount and getting interest in the additional amount also

It is beneficial if the frequency of compounding is more or compounding in less time is more beneficial

For eg if we invest 100at 10 % compounding year we will get 110 at the end of year

If same 100 and same interest 10% but compounding half yearly means 100*1.05 at the end of 6 months 105 and we will get interest on 105 for the rest of the period that is 6 months so 105*1.05=110.25 so we are getting 0.25 more

Borrowers pay interest and lenders collect interest as the effects be interest rate is more if the compounding frequency is more by observing the above example . So the interest payer will loose and interest recover will gain means borrower will lose and lender will gain.

C) the required amount is given means future value was given in the problem and rate is given at 6% and time 12 years we have to calculate the required amount to deposit now means at present to get the required amount of 50000$ after 12 years

We should calculate the present value of 50000$

50000*Present value interest factor at 6% for 12years

= 50000*0.497=$24848

Should invest at 6% to get $50000 after 12 years