# Basic Finance: Annuities, Interest Rates, Rates of Return

1. Determine the future value of an annuity that pays $5,000 at the end of the next 11 years. Similar securities pay an interest rate of 7%.

2. How much money would you be willing to pay in order to receive $800,000 40 years from today? Assume that your required rate of return on investments is 8% compounded semiannually.

3. You are currently making $300 monthly payments on a $12,000 7% fixed interest loan that compounds interest monthly. At this rate how long will it take you to repay your loan?

4. You buy a home for $295,000 with a 15 year fixed mortgage that has an 8.75% interest rate compounded monthly. Determine (1) the monthly payment, and (2) the total interest, principle, and total cash outflow at the end of 1 year.

5. Your friend Jack hires ABC Lawn Service to trim the hedges in his garden. There are three payment options with the company. Which of the following three options should Jack choose if he can earn 8% interest compounded quarterly on his money?

a. Option 1 Pay $5650 cash immediately

b. Option 2 Pay $6750 in one lump sum two years from now

c. Option 3 Pay $800 at the end of each quarter for two years

6. Your boss wants to know which project had a better return. She says that Project Y returned $7,560 today on a $2,200 investment three years ago (use annual compounding for Project Y). She also says that Project Z returned $9,887 today and required investments of $367 each quarter for the last three years. Which project has a higher return?

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The answers are in the attached file

1. Determine the future value of an annuity that pays $5,000 at the end of the next 11 year. Similar securities pay an interest rate of 7%.

The question is not very clear. 5000 is paid at the end of next 11 year then that is the future value or if we take annuity value as 5000 per year and find the FV of this annuity at 7% interest. For this purpose we an use the FVIFA table and get the value for 11 years at 7%, this is 15.784 and hence the FV is 5000*15.784= $78920

2. How much money would you be willing to pay in order to receive $800,000 40 years from today? Assume that your required rate of return on investments is 8% compounded semiannually.

In this case we are required to find the present value of an investment which will grow to 800,000 in 40 years compounded at the rate of 8% semiannually. We can use the compound interest formula to calculate the present value.

The formula is a s below

CI= P*(1+r/100)n

Where CI is the future value, P is the present value, r is the interest rate and n is the no. of years. In the present case -

CI=800,000, P=?, r=8% and n= 40

Since the compounding is semiannual, we need to divide the interest rate by 2 and multiply the period by 2, we get r=4% and n=80. Putting in the formula we get

800000 = P*(1+0.04)80

solving this equation, P= 800000/(1.04)80 give P = 800000*0.043384

P= 34707.46

3. You are currently making $300 monthly payments on a $12,000 7% fixed interest loan that compounds interest monthly. At this rate how long will it take you to repay your loan?

We need to find the number of months required to repay a loan of 12,000 taken at 7% interest ...

#### Solution Summary

The solution explains how to calculate annuities, interest rates and rates of return for time value of money problems

Basic Concepts in Finance: Time Value of Money

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Q5-7

DR. FRANKENSTEIN IS CONSIDERING BUILDING A PORTFOLIO CONTAINING TWO ASSETS, S AND G.

ASSET S WILL REPRESENT 70% OF THE DOLLAR VALUE OF THE PORTFOLIO, AND ASSET G WILL REPRESENT THE REMAINING 30%. THE EXPECTED RETURNS OVER THE NEXT 5 YEARS 2001-2005, FOR EACH OF THESE ASSETS IS SHOWN BELOW:

EXPECTED RETURN

YEAR ASSET S ASSET G Expect. Port. Return Expect. Value of Port. Std. Deviation.

2001 15% 15%

2002 16% 14%

2003 17% 13%

2004 19% 11%

2005 21% 9%

5. CALCULATE THE EXPECTED PORTFOLIO RETURN, k p, FOR EACH OF THE 5 YEARS.

6. CALCULATE THE EXPECTED VALUE OF PORTFOLIO RETURNS, k p, OVER THE 5-YEAR PERIOD.

7.CALCULATE THE STANDARD DEVIATION OF EXPECTED PORTFOLIO RETURNS, s k p, OVER THE 5-YEAR PERIOD.

Q8-10

James Snooka is building a portfolio containing two assets, S and P. Asset S will represent 70 Percent of the dollar value of the portfolio, and asset P will account for the other 30 percent. The expected returns over the next 8 years, 2002 - 2009, for each of these assets, are shown in the following table:

Expected Return

Year Asset S Asset P Exp. Port. Ret. Expect. Value Std. Dev.

2002 15% 20%

2003 15 17

2004 17 15

2005 18 14

2006 18 14

2007 19 14

2008 20 12

2009 20 10

8. Calculate expected portfolio return kp, for each of the 8 years.

9. Calculate the expected value of portfolio returns kp over the 8 year period.

10. Calculate the standard deviation of expected portfolio returns, skp, over the 8 year period.

Q11-20

10. - 15. Calculate the present value of the annuity assuming that it is an ordinary annuity.

16-20. Calculate the present value of the annuity assuming that it is an annuity due.

Case Amount of Annuity Interest Rate Period / Years

A $14,000 9% 3

B $17,500 13% 15

C $975 18% 7

D $1,127,000 4% 9

E $10,000 7% 3

21- 25. Calculate the future value of the annuity assuming that it is an ordinary annuity.

26-30. Calculate the future value of the annuity assuming that it is an annuity due.

Case Amount of Annuity Interest Rate Period / Years

A $42,000 4% 7

B $77,500 11% 13

C $975,000 17% 11

D $27,000 20% 16

E $1,000 7% 4

Albertus Magnus College wishes to set Prof. Sulkis up for life with a jumbo bonus upon his retirement. By contract Mike will retire at the end of 22 years. Upon retirement, he is entitled to receive a bonus payment of $750,000. If he dies prior to retirement, the bonus will pass to his three heirs; Bud, Weis and Er.

During the 22-year "accumulation period" Albertus wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 11% interest.

A) How large must Albertus's equal annual end-of-year deposits into the account be over the 22-year accumulation period to fully fund Prof. Sulkis's retirement bonus?

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