PLEASE SHOW ALL WORK 1. (calculating the future value of an annuity) If you inve

Question

PLEASE SHOW ALL WORK

1. (calculating the future value of an annuity) If you invest $100 a year for 20 years at 6% annual interest, how much will you have at the end of the 20th year?

2. (calculating the present value of an annuity) How much would you be willing to pay today for an investment that pays $700 a year at the end of the next 5 years? (Your required rate of return is 6% a year.)

3. (Rate of return of an annuity) You would like to have $1,000,000 40 years from now, but the most you can afford to invest each year is $1,000. What annual rate of return will you have to earn to reach your goal?

4. (Monthly compounding) If you bought a $1,000 face value CD that matured in six months, and which was advertised as paying 6% annual interest, compounded monthly, how much would you receive when you cashed in your CD at maturity?

5. (Annualizing a monthly rate) Your credit card statement says that you will be charged 1.03% interest a month on unpaid balances. What is the Effective Annual Rate (EAR) being charged?

6. (Monthly loan payment) Best Buy has a flat-screen HDTV on sale for $1,799. If you could borrow that amount from Carl's Credit Union at 6% for 1 year, what would be your monthly loan payments?

7. (PV of a perpetuity) If your required rate of return was 6% a year, how much would you pay today for $100 a month forever? (that is, the stream of $100 monthly payments goes on forever, continuing to be paid to your heirs after your death)

8. (PV of an uneven cash flow stream) what is the PV of the following project? (Assume r = 7%) Year Cash Flow

1 -$1,000

2 - $2,000

3 - $3,000

4 $4,000

9. (FV of an uneven cash flow stream) what is the FV at the end of year 4 of the following project? (Assume r = 7%) Year Cash Flow

1- $1,000

2 - $2,000

3 - $3,000

4 - $4,000

Explanation / Answer

1

Present value of annuity = 100*(1-1/1.06^20)/6%= 1146.99

You will have at the end of the 20th year = 1146.99*1.06^20=   $3,678.56

2.   

present value of an annuity = 700*(1-1/1.06^5)/6%= 2,949

3.

Present value of 1000000 = 1,000,000/(1+r)^40

Present value of annuity = 1,000,000/(1+r)^40

1,000,000/(1+r)^40 = 1000*(1-1/(1+r)^40)/r

r= 12.95%

4.   

Receive at maturity =1000*(1+6%/12)^6= 1030

5.

Effective Annual Rate (EAR) being charged = (1+1.03%)^12-1= 13.08%

6.

Let monthly loan payaments = x

Present value payaments = $1799

1799 = x*(1-1/(1+6%/12)^12)/(6%/12)

X= $154.83

7.   

pay today = 100/(6%/12)= $20000

8.

PV of the following project = 1000/1.07 +2000/1.07^2 +3000/1.07^3 +4000/1.07^4=   $8182

9.

FV at the end of year 4 of the following project = 1000*1.07^3 + 2000*1.07^2 + 3000*1.07^1 + 4000=10724.84

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