Question

You have decided to invest in a new business venture that will likely to pay you $800 at the end of each month for the next 10 years. You believe that a reasonable rate of return on your investment should be an annual rate of 12% compounded monthly. How much should you pay for the investment? What will be total amount of cash you will receive over the next 10 years? What do you call the difference?

Answer 1

Part A:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$               800.00
Int Rate	1.0000%
Periods	120

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 800 * [ 1 - [(1+0.01)^-120]] /0.01
= $ 800 * [ 1 - [(1.01)^-120]] /0.01
= $ 800 * [ 1 - [0.303]] /0.01
= $ 800 * [0.697]] /0.01
= $ 55760.42

Part B:

Total Cash = $800 * 10 * 12

= $ 96000

PartC:

The difference is called as Time value of money.