Question

1- Calculate the present value of $35,000 received 9 years from today if your investment pays 6% compounded annually.                                                                                                      

2- Calculate the present value of $50,000 received 8 years from today if your investment pays 8% compounded semiannually.                                                                                               

3- Calculate the present value of annuity $70,000 received 20 years from today if your investment pays 7% compounded annually.

                                                                                   

4- Calculate the present value of annuity $30,000 received 8 years from today if your investment pays 8% compounded quarterly.     

5- Calculate the future value of an annuity stream that pays $15,000 every year for 6 years on the last day of each year if your investment pays 12% compounded quarterly.

6- Calculate the future value of an annuity stream that pays $10,000 every year for 12 years on the last day of each year if your investment pays 6 % compounded semiannually.

7- Calculate the Future value of $35,000 received 9 years from today if your investment pays 6% compounded annually.   

8- Calculate the Future value of $75,000 received 8 years from today if your investment pays 8% compounded semiannually.                                                                                              

                                                                                                

9- Calculate the present value of annuity $30,000 received 8 years from today if your investment pays 8% compounded yearly.    

10- Calculate the present value of annuity $150,000 received 150 years from today if your investment pays 9% compounded annually.                                                                               

                                                                    

Answer 1

Present Value = Future Value / (1 + r)ⁿ

If there is compounding monthly, quarterly or semiannually then we divide r by compounding(12 in case of monthly, 4 in case of quarterly and 2 in case of semiannually) and multiply n to compounding (12 in case of monthly, 4 in case of quarterly and 2 in case of semiannually)

1. Future value = 35000

n = 9

r = 6%

Compounding (m) = 1 (because compounding is annually)

Present value = 35000 / (1 + 0.06)⁹

= 35000 / 1.6895

= $20716.45

2. Future Value = 50000

m = 2

n = 8 yrs = 8*2 = 16

r = 8% = 8% / 2 = 4%

Present Value = 50000 / ( 1 + 0.04)¹⁶

= 50000 / 1.87298

= $26695.41

3. Annuity = 70000

n = 20 yrs

r = 7%

m = 1

Present Value of annuity = Annuity * [{1 - (1 / (1 + r)^n)} / r]

= 70000 * [{1 - (1 / (1 + 0.07)^20)} / 0.07]

= 70000 * 10.59401

=$741,581

4.

Annuity = 30000

n = 8 yrs = 8*4 = 32

r = 8% = 8%/4 = 2%

m = 4

Present Value of annuity = Annuity * [{1 - (1 / (1 + r)^n)} / r]

= 30000 * [{1 - (1 / (1 + 0.02)^32)} / 0.02]

= 30000 * 24.46833

=$704,050