Question

A new investment opportunity for you is an annuity that pays $3,350 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
Select the correct answer.
a. $9,564.37
b. $9,593.57
c. $9,549.77
d. $9,578.97
e. $9,535.17

Answer 1

Answer:

Answer: e. 9535,17

The annuity pays $3350 at the beginning of each year during 3 years, which means that if you decide to invest on it, you could receive $3350 now (at moment 0), $3350 at the beginning of the next year (let’s say at the beginning of moment 1) and $3350 in two years (at the beginning of period 2).

To be able to know how much does those payments (that are going to happened in the future) worth today, one should discount futures values to moment zero. One could easily think of these payments as if they were three bank checks that worth $3350 each, to be paid in the dates mentioned before: at moment zero (now), in a year (moment 1) and in two years (moment 2). If one decided to go to a bank and ask the bank to have money in advanced using these three checks, the bank would gives us the equivalent of the checks' present value, which is  

$Present Value= 3350 + \frac{3350}{1+0.055} +\frac{3350}{(1+0.055)^2}$

Step-by-step explanation:

• Take into account that times worth: is not the same 1 dollar today that one dollar into one year. This is why we use discount operation to express all values in terms of the same moment of time (that usually is moment zero).
• Use discount to calculate present values: this consists on dividing future values by $(1+i) ^ n$, where i is the interest rate and n is the temporary distance between the future value and moment zero (if the payment is going to happend in year 2, n=2).
• After discounting all futures values using the correct interest rate and the proper "n" for each future value, sum up all discount values, and you will have the present value of your future cash flow.