Present Worth Midterm 1 question

From Midterm 1, Form C Question 15.

Consider the asset below

YEAR BENEFIT
0 0
1 1
2 2
3 3
4 4
5 4
6 4
7 4
8 4
9 3
10 2
11 1

When the interest rate is 10%, what is the present worth of the benefits in periods five through eight?

A) $13.66
B) $12.68
C) $8.66
D) $20.00
E) None of the Above

The correct answer is C, $8.66.
P= 4(P/A i=10% n=4)

Use the constant series formula for P given A, A being the constant which in this case= 4

P= 4((1.104) -1)/( (1.104).1 (1.104))= 8.66

Note: One must further divide by (1 + i) raised to n number of periods that would discount the value back to time period zero. If one fails to do this, one ends up with the incorrect answer of $12.68. If one simply sums the benefits in periods four through eight, one finds the incorrect answer of $20.00. It is unclear how to arrive at the incorrect answer of $13.66.

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