Part I: Sensitivity of PV with respect to r and t

Find the present value (PV) of $25,000 (= FV) at a discount rate (r or I) of 0%, 1%,

2%,…50%. That is, vary your discount rate between 0 and 50% in jumps of 1% (51 total

answers). Assume a time t of 10 years.


Present your analysis in a table.

Make a graph of your table (relationship between discount rate and present values).

Explain what the graph tells in a textbox below the graph.

Is this relationship linear? How does PV change when r changes?

Do the same for the relationship between PV and time t.

Find the present value of $25,000 at a discount rate of 10% assuming that this future value of

$25,000 is lying 0 year in future, 1 year ahead (in future), 2 years, ... , 50 years. That is find the

PV of $25,000 at 10% r, changing t from 0 to 50 (51 answers).


Make a table and a graph of this t and PV relationship.

Explain in words what the graph and table tells you about what happens to PV when t changes.

For bonus points: Do a two-way sensitivity by changing both r and t and creating a two table

(matrix) of answers. Plot the resulting two-way table in a 3-D graph in Excel and

explain what it tells you in words.


Part II: Sensitivity of Annuity PV with respect to, r, t and PMT.

Make a table and graph (as above) for the present value of an annuity with 30 years life

and annuity payment of $5,000 at discount rates from 0% to 50% in jumps of 1% (51


Each of these answers represents how much you can borrow at a given r if you pay the amount

back in 30 years in equal installments of $5,000 per year.

Make a similar table and graph as above but this time, calculate the future value of

annuity instead of its present value.

This is the amount you will have after 30 years by saving $5,000 each year provided that you get

a rate of return equal to each r you use in the table.


Find the payment you would need to make (i.e., money you need to save) per year at a

discount rate (in this case, your rate of return) of 0% to 50% in jumps of 1% (51

answers), if want to have saved up a grand sum of $5,000,000 after the next 30 years

(FV). Make a table and graph of your answers.


Explain in words the results of this numerical analysis in a way that will make sense to your

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