Question

ssume your employer offers a bonus of $7,500. The only catch is that you must wait 6 years to take possession of the money. If you can earn 4% on your savings, what is the minimum you would take today to match the bonus? (Round your answer.) $5,900.

Answer 1

Answer:

$5,927.36, or $5,900.

Explanation:

• In this particular problem, we are given a future value of $7,500 (C = $7,500), which is to be received after 6 years, that is, we have an n = 6 years.
• Since $7,500 is a bonus that is to be received in the long term, we know that we could match its monetary value by saving a lesser amount of money for 6 years, accumulating earnings of 4% every year.
• How do we calculate this lesser amount of money? We make use of a useful formula for present value (PV):

$PV=\frac{C}{(1+r)^{n} }$

-Where PV: Present value (let's say its the equivalent amount of money of C, but in the present. That is, the amount of money that we should take today to match the bonus of $7,500 after 6 years),

-C: Cash flow at a given period of time (in this case, the $7,500 that were to be received after 6 years),

-r: Interest rate (the percentage that is going to be earned on our savings each year, 4%), and

-n: Number of periods of time that will have passed (in this case, we are talking about 6 years).

So, to know what is the minimum that we would take today to match the bonus, we have to apply the above formula, and substitute the values that we have (C=$7,500, r=4% or 0.04, and n=6 years).

$PV=\frac{7500 dollars}{(1+0.04)^{6}}\\PV=\frac{7500 dollars}{(1.04)^{6}}\\PV=\frac{7500 dollars}{1.265}\\PV=5927.359dollars$

So our present value is approximately of PV≈$5,900, which is the amount of money that we would have to take today to match the bonus of $7,500 after 6 years of saving.