Question

1. Suppose that for each of the next 10 years you will receive $250. If the opportunity cost of capital is 5% how much is this stream of cash flows worth today?  

2.Suppose that you deposit $450 in the bank at the end of each of the next 10 years. If the APR is 1% how much will be in your account at the end of 10 years?

3.Suppose that starting one year from now you will receive $100 a year at the end of every year. If the discount rate is 6% what is this stream of cash flows worth today?

4.Suppose that you will receive $200 at the end of every year starting 5 years from now (i.e. first payment EOY 5). What is this stream of cash flows worth if the cost of capital is 7%?

Answer 1

PV of annuity

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity = P[1- (1+ r)^-n]/ r

= 250[1- (1+ 0.05)^-10]/ 0.05

= 250[1- (1.05)^-10]/ 0.05

= 250[1- 0.613913253540759]/ 0.05

= 250[0.386086746459241/ 0.05]

= 250[7.72173492918481]

= 1930.43

So PV of the amount after 10 years is 1930.43

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FV of annuity

Annuity is series of equal cash flows for certain period of time, if periodic cash flow is P, number of period is n, and interest per period is r then future value of cash flow will be

FV of annuity = P [(1 + r)^n - 1]/ r

Let's put the values in the formula,

= 450[(1 + 0.01)^10 - 1]/ 0.01

= 450[(1.01 )^10 - 1]/ 0.01

= 450 ( 1.1046221254112 ) - 1/ 0.01

= 450 ( 0.104622125411205 )/ 0.01

= 450 * 10.4622125411205

= 4707.99564350421

So FV of 450 received for 10 period is 4708

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Hope this answer your query.

Feel free to comment if you need further assistance. J