Value of a single amount versus a mixed stream Personal finance problem Gina Via
ID: 2781313 • Letter: V
Question
Value of a single amount versus a mixed stream Personal finance problem Gina Viale has just contracted to sell a small parcel of land that she inherited a ago. The buyer is willing to pay $24,582 at the closing of the transaction or will pay the amounts shown in the following table, EB. at the beginning of each of the net five years Because Gina doesn't really need the money today, she plans to let it accumulate in an account that earns 7% annual interest Given her desre to buy a house at the end of five years after closing on the sale of the lot, she decides to choose the payment alternative-$24,582 single amount or the mbxed stream of payments in the table- that provides the higher future value at the end of 5 years. Which alternative will she choose? The future value. Fvn, of the lump sum deposit is S (Round to the nearest cent) The future value of the mixed stream of payments is s (Round to the nearest cent) Which alternative will Gina choose? (Select the best answer below.) O Mixed stream of payments Lump sum deposit O Data Table (Click on the icon located on the top-right comer of the data table below in order to copy its contents into a spreadsheet.) Mixed Stream Beginning of year Cash Flow $2,000 $9,000 $8,000 $8,000 $4,000 Print DoneExplanation / Answer
Future value of lump sum deposited at 7 % interest for 5 year compounding annually:
Formula for compound interest:
A = P x (1 +r/n)nt
Where,
A = Amount after maturity
P = Principal amount = $ 24,582
r = Rate of interest = 7 % or 0.07 p.a.
n = Frequency of compounding in a year =1
t = no. of years = 5
A =$ 24,582 x (1+0.07)5
= $ 24,582 x (1.07)5
= $ 24,582 x 1.402552
= $ 34,477.53
Future value of cash flows:
Formula for future value of uneven annuity due is:
FV = CF1 x (1+r)n + CF2 x (1+r)n-1 + ….+ CFn x (1+r)n-n
Putting the values in above formula we get FV as:
Year
Cash flow
Future value
1
$ 2,000
$ 2,805.10
2
$ 9,000
$ 11,797.16
3
$ 8,000
$ 9,800.34
4
$ 8,000
$ 9,159.20
5
$ 4,000
$ 4,280.00
Total
$ 37,841.81
Answer:
Future value of lump sum deposit is $ 34,477.53
Future value mixed stream of payment is $ 37,841.81
Gina should choose mixed stream of payment which give more amount than lump sum deposit.
Year
Cash flow
Future value
1
$ 2,000
$ 2,805.10
2
$ 9,000
$ 11,797.16
3
$ 8,000
$ 9,800.34
4
$ 8,000
$ 9,159.20
5
$ 4,000
$ 4,280.00
Total
$ 37,841.81
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