Midterm 1 Simple Time Shift

Midterm 1 Simple Time Shifting Example

Q: Assuming an interest rate of 10% what is the present worth of the part of an asset that gives you \$100 per year for 40 years beginning in year 2?

a) \$889.00
b) \$977.91
c) \$808.19
d) \$973.27

Explanation:
This problem becomes straightforward once you interpret what type of structure the question is describing. A constant benefit of \$100 per year clearly suggests a constant series calculation, but to get the correct answer the proper time shift needs to be applied.
Drawn out the series would look like this;

Ignoring the position of the series on the timeline the present worth of the series can be written in factor notation as;
P(1)= \$100(P/A,10%,40)
P(1)=\$100* (((1+.1)^40-1)/(.1*(1+.1)^40))
P(1)=977.91

But this is not the present (t=0) value, instead it is the value collected at time t=1;

To get the value at time t=0 it must be shifted one period to the past (N=1).
P(0)=P(1)/(1+i)^N
P(0)=977.91/(1+.1)^1
P(0)=\$889.00