Question

 Personal finance problem   Gina Vitale has just contracted to sell a small parcel of land that she inherited a few years ago. The buyer is willing to pay

​$24 , 000

​now, or the buyer will make a series of payments starting now and continuing at annual intervals shown in the following​ table,

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.

Because Gina​ doesn't really need the money​ today, she plans to let it accumulate in an account that earns

77​%

annual interest. Given her desire to buy a house five years after selling the​ lot, she decides to choose the payment

alternativelong dash—either the lump sum or the mixed streamlong dash—that

provides the higher future value at the end of 5 years. Which alternative will she​ choose?

Begining of the year/ Cash flow

0 $2000

1 $4000

2 $6000

3 $8000

4 $10,000

The future​ value, FV Subscript nFVn​, of the lump sum deposit is

The future value of the mixed stream of payments is

​

Answer 1

Future value is the amount which would be received in future.
The interest rate is given as 77% pa and thus the same is considered to calculate future value.
Calculation of future value of lump-sum deposit
Future value	Amount*(1+r)^n
r is interest rate and n is time period.
Future value	24000*(1.77^5)
Future value	24000*17.37266
Future value	$416,943.85
Thus, future value of lump-sum deposit is $416,943.85.
Calculation of mixed stream long dash future value
Year	Cash flow	Future value factor		Future value (Cash flow*Future value factor)
0	$2,000	17.37266	(1.77^5)	$34,745.32
1	$4,000	9.81506	(1.77^4)	$39,260.25
2	$6,000	5.54523	(1.77^3)	$33,271.40
3	$8,000	3.13290	(1.77^2)	$25,063.20
4	$10,000	1.77000	(1.77^1)	$17,700.00
				$150,040.17
Thus, future value of mixed stream cash flow is $150,040.17.
Gina would prefer lump-sum deposit over mixed stream cash flow as the future value of lump-sum amount is higher.