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2 years ago

7

Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)

1 answer:

vredina [299]2 years ago

3 0

Answer:

value: $66,184.15
interest: $6,184.15

Step-by-step explanation:

The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.

__

<h3>formula</h3>

The formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...

FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)

FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148

FV ≈ 66,184.15

<h3>calculator</h3>

The attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.

__

<h3>a) </h3>

The future value of the annuity due is $66,184.15.

<h3>b)</h3>

The total interest earned is the difference between the total of deposits and the future value:

$66,184.15 -(12)(5000) = 6,184.15

A total of $6,184.15 in interest was earned by the annuity.

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Step-by-step explanation:

Problem One (left panel)

<em><u>Question A</u></em>

The y intercept happens when x = 0
That being said, the y intercept is 50. It was moving when the timing began.

<em><u>Question B</u></em>

The rate of change = (56 - 52)/(3 - 1) = 4/2 = 2 miles / hour^2 (you have a slight acceleration.

<em><u>Question C</u></em>

60 = a + (n-1)d
60 = 50 + (n - 1)*2
10/2 = (n - 1)*2/2
5 = n - 1
6 = n

The way I have done it the domain is n from 1 to 6

Question 2 (Right Panel)

<em><u>Question A</u></em>

The equation for the table is f(x) = 3x - 3 which was derived simply by putting all three points into y = ax + b and solving.

f(0) = ax + b
-3 = a*0) + b
b = - 3
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f(x) = ax - 3
f(-1) = a*(-1) - 3 but we know (f(-1)) = -6
- 6 = a(-1) - 3 add 3 to both sides
-6 +3 = a(-1) -3 + 3
-3 = a*(-1) Divide by - 1
a = 3
f(x) = 3x - 3 Answer for f(x)
The slope of f(x) = the coefficient in front of the x
f(x) has a slope of 3
g(x) has a slope of 4

<em><u>Part B</u></em>

f(x) has a y intercept of - 3
g(x) has a y intercept of -5
f(x) has the greater y intercept.
-3 > - 5

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