Question

Suppose you receive ​$100100 at the end of each year for the next three years. a. If the interest rate is 9 %9%​, what is the present value of these cash​ flows? b. What is the future value in three years of the present value you computed in ​(a​)? c. Suppose you deposit the cash flows in a bank account that pays 9 %9% interest per year. What is the balance in the account at the end of each of the next three years​ (after your deposit is​ made)? How does the final bank balance compare with your answer in ​(b​)?

Answer 1

a)

	Present value of these cash​ flows	P×[1-(1÷(1+r)^n)]÷r
	Here,
A	Interest rate per annum	9.00%
B	Number of years	3
C	Number of compoundings per per annum	1
A÷C	Interest rate per period ( r)	9.00%
B×C	Number of periods (n)	3
	Payment per period (P)	$                                             100
	Present value of these cash​ flows	$          253.13
		100×(1-(1÷(1+9%)^3))÷9%

b)

	Future value of these cash​ flows	P×[(1+r)^n-1]÷r
	Here,
A	Interest rate per annum	9%
B	Number of years	3
C	Number of payments per per annum	1
A÷C	Interest rate per period ( r)	9%
B×C	Number of periods (n)	3
	Payment per period (P)	$                                  100
	Future value of these cash​ flows	$    327.81
		100×((1+9%)^3-1)÷9%

c)

Year	Opening balance	Deposit	Interest	Closing balance
0	$                           -	$              -	$                -	$                         -
1	$                           -	$     100.00	$                -	$               100.00
2	$                  100.00	$     100.00	$           9.00	$               209.00
3	$                  209.00	$     100.00	$         18.81	$               327.81