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.
1 answer:
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
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
, 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.
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Answer:
(y equals start fraction two over three end fraction x)
Step-by-step explanation:
Lest's organize the table values of our function first:
x y
-6 -4
-3 -2
0 0
3 2
The simplest kind of of function is a linear function of the form where
is the slope and
is the y-intercept. Let's us check if our function is a linear one finding its equation and checking that all points are in the line.
The first step to find a linear equation is find the slope of the line; to do it, we are using the slope formula:
where
is the slope of the line
are the coordinates of the first point
are the coordinates of the second point
We know from our table that the first and second points are (-6, -4) and (-3, -2) respectively, so ,
,
, and
.
Replacing values:
Now that we have the slope of our line we can use the point slope formula to complete our linear function:
where
is the slope
are the coordinates of the first point
Replacing values:
Now, to check if our function is valid, we can either check if each point satisfies the rule , or we can graph it and check if each lies is in the graph.
Let's check both:
We already know that points (-6, -4) and (-3, -2) satisfy the rule (after all, those were the point we used to came out with the rule in the first place), so we just need to check the points (0, 0) and (3, 2)
- For (0, 0):
The point satisfies the rule.
- For (3, 2):
The point satisfies the rule.
Since all the points of our table satisfies the rule , we can conclude that the rule describing the function shown is
.
