1).We need to find present value of all amounts under 3 options.

PV of $ 1000 in hand today is = $ 1000

PV of $ 2000 due in 6 years is = 2000/(1+0.14)^6

= 2000*0.4556 = $ 911

PV of $ 5000 due in 10 years is, = 5000/(1+0.14)^10 = 5000*0.2697= $1348.5

We can see that $ 5000 due in 10 years has more value today than remaining all

It is because $ 1000 today if compounded for 10 years at 14% , it becomes 1.14^10 = 3.707 times the original amount after 10 years ...which means it becomes $ 3707

And if $ 2000 due in 6 years compounded for remaining 4 years...it will become 1.14^4 = 1.6889 times the original amount after 10 years..which means it becomes 3378 after 19 years...Both are less than $ 5000

2).Equal Annual installment payable for each year can be found uisng present value of annuity factor....

Equal installment = present value of loan/ PVAF

1500 = 18,000/PVAF(3%,n)

PVAF(3%,n) = 12

We can find the n value in PVAF table by searching for PVAF of 12 in 3% interest column for matching year.

We can see that the PVAF value of 12 lies between 15 and 16 years.

So it takes nearly 16 years to repay the loan.

3).A.The client invests $ 6000 at the end of each until he attains age of 65 ...which means for 25 years he invest $6000 each year.

The amount he will get at his age of 65 can be found using future value of annuity factor

Future value = annual payment* FVAF(12%,25)

= 6000* 133.3339

= $800,003.4

He will get $ 800,003.4 at his age of 65 years

B.We can see that by investing $6000 each year ,he had $ 800,003.4 at his age of 65.

Now instead of withdrawal ,he wants yearly pension. Yearly pension amount can be found using present value of perpetuity formula.

Present value of perpetuity = cash flow per period/ interest rate per period

$ 800,003.4 = yearly pension/ 0.05

Yearly pension = 800,003.4*0.05

= $ 40,000.17

4).Land value in 1981 = $ 200,000

Land value in 2005 = $ 1,582,200

In 15 years ( it is assumed land valued at end of 2005) the land value increased by $1,382,200

We can find annual appreciation rate by using compound interest formula

Amount = principal * (1+r)^n

1,582,200 = 200,000*(1+r)^15

(1+r)^15 = 7.911

1+r = 7.911^(1/15)

1+r = 1.14784

r = 0.14784 or 14.78%

Annual appreciation rate is 14.78%

If we assumed land valued at beginning of 2005 ,total holding period of land is 14 years only.

Then

(1+r)^14 = 7.911

1+r = 7.911^(1/14)

1+r = 1.1592

r = 0.1592 or 15.92%

Annual appreciation rate is 15.92%

5) Present value of bonus that will be received after 10 years can be calculated as below,

Present value = future value/(1+r)^n

= 5000/(1+0.12)^10

= $ 1610

Present value of bonus is $ 1610

6) We can use compound interest formula to caluculate annual rate.

Amount = principal * (1+r)^n

Where r is interest per period which in our problem is per quarter

n is number of times compounded( since it is compounded for each quarter i.e each 3 months, then in total 60 months it will be compounded 20 times)

  1801 = 1000(1+r)^20

(1+r)^20 = 1.801

1+r = 1.02985406

r = 0.02985406

The above interest is per quarter....

Annual interest rate = 0.02985406*4 = 0.1194 or 11.94%

7) We can find amount after 10 years using future value of annuity formula.Since amount of $ 30,000 deposited each quarter.

Interest rate per quarter = 0.08/4 = 0.02

Number of periods it is compounded = 10*4 =40

Future value = cash flow per period* FVAF(2%,40)

= 30,000* 60.40198

= $ 1,812,059.4

Amount in the fund after 10 years is $ 1,812,059

Please see the attached file for the complete solution