Question

Value of a mixed stream For the mixed stream of cash flows shown in the following​ table, LOADING...​, determine the future value at the end of the final year if deposits are made into an account paying annual interest of 13​%, assuming that no withdrawals are made during the period and that the deposits are​ made:

1              30,300

2              25,250

3              20,200

4              10,100

5              5,050

a. At the end of each year.

b. At the beginning of each year.

a. The future value at the end of the final year if deposits are made at the end of each year is ​$

b. The future value at the end of the final year if deposits are made at the beginning of each year is ​$

Answer 1

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a. The future value at the end of the final year if deposits are made at the end of each year is ​ $ 128078.53

Working,

Year	CashFlows
1	30,300
2	25,250
3	20,200
4	10,100
5	5,050

Using concepts from the time value of money,

Future Value = Present Value (1+ r)t

where t is the time period and r represent the interest rate

Here Annual interest rate,r = 13% or 0.13

Therefore

Future value at the end of the final year(deposits are made at end of the year) =

= 30,300 X (1.13)4 + 25,250 X (1.13)3 + 20,200 X (1.13)2 + 10,100 X (1.13)1 + 5,050 X (1.13)0

= 30,300 X 1.63 +  25,250 X 1.44 + 20,200 X 1.28 + 10,100 X 1.13 + 5,050 X 1

= 49389 + 36433.15 + 25793.38 +11413 + 5050

= $ 128078.53

b. The future value at the end of the final year if deposits are made at the beginning of each year is ​$ 144733.00

Working

Similarly using the concept of the time value of money,

Future value at the end of the final year(deposits are made at begining of the year) =

= 30,300 X (1.13)5 + 25,250 X (1.13)4 + 20,200 X (1.13)3 + 10,100 X (1.13)2 + 5,050 X (1.13)1

= 30,300 X 1.84 +  25,250 X 1.63 + 20,200 X 1.44 + 10,100 X 1.28 + 5,050 X 1.13

= 55825.79 + 41157.50 + 29146.52 + 12896.69 + 5706.50

= $ 144733.00