Question

1. If you invest $1,000 today at an interest rate of 10% per year, how much will you have 20 years from now, assuming no withdrawals in the interim?
2. What is the present value of the following cash flows at an interest rate of 10% per year?
   1. $100 received five years from now.
   2. $100 received 60 years from now.
   3. $100 received each year beginning one year from now and ending 10 years from now.
   4. $100 received each year for 10 years beginning now.
   5. $100 each year beginning one year from now and continuing forever. (Hint: You do not need to use the financial keys of your calculator for this, just some common sense.)

Answer 1

Amount Invested today = $ 1000

Interest rate = 10% per year

- Calculating the future Value at the end of 20 years:

future Value = $ 6727.50

e present value of the following cash flows at an interest rate of 10% per year?

1. $100 received five years from now.
2. $100 received 60 years from now.
3. $100 received each year beginning one year from now and ending 10 years from now.
4. $100 received each year for 10 years beginning now.
5. $100 each year beginning one year from now and continuing forever. (Hint: You do not need to use the financial keys of your calculator for this, just some common sense.)

a). Calculating the present value of $ 100 received five years from now:

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

= 100/(1+0.10)^6

= $ 62.09

b). Calculating the present value of $ 100 received 60 years from now:

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

= 100/(1.10)^60

= $ 0.3284

c). Calculating the present value of $100 received each year beginning one year from now and ending 10 years from now:

Where, C= Periodic Payments = $100

r = Periodic Interest rate = 0.10

n= no of periods = 10

Present Value = $ 614.46

d). Calculating the present value of $100 received each year for 10 years beginning now:

Where, C= Periodic Payments = $100

r = Periodic Interest rate = 0.10

n= no of periods = 10

Present Value = $ 675.90

e). Calculating the Present value of $100 each year beginning one year from now and continuing forever:

Present Value = Cashflows/interest rate

= $100/10%

= $1000

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