A pyramid has a base area of 60.5 cm^2 and a height of 12 cm what is the volume of the pyramid

ION 1: BASIC ANNUITIES AND APPLICATIONS [20 MARKS]

DENIUS [597]

Answer:

Find the present and future value of $1000 received every month end for 20 years if the interest rate is J12 = 12%

$90,819.42

Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years.

$26,935.64

1. John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

$178.7644 ≈ $178.76

Step-by-step explanation:

there are two ways to solve this question:

using the formula for present value of annuity
using an annuity table

since this question is about monthly payments, I will use the annuity formula:

PV = payment x {[1 - (1 + r)⁻ⁿ]/r}

PV = 1000 x {[1 - (1 + 0.01)⁻²⁴⁰]/0.01}

r = 12% / 12 = 1%

n = 20 x 12 = 240

PV = $90,819.42

for the annuity due, we can use an annuity table since payments are annual:

payment $10,000

20 years

12% interest rate

PV annuity due = $10,000 x 8.3658 = $83,658

since the first payment is received 10 years form now, we must determine the PV = $83,658 / (1 + 0.12)¹⁰ = $26,935.64

1)

monthly payment = total amount / discount factor

total amount = monthly payment x discount factor

monthly payment = 2,000
discount factor = D = {[(1 + r)ⁿ] - 1} / [r(1 + r)ⁿ] = D = {[(1 + 0.005)¹⁸⁰] - 1} / [0.005(1 + 0.005)¹⁸⁰] = 1.45409 / 0.01227 = 118.5032

total amount = $237,006.45

we have to divide John's account in two:

the future value of $10,000 = $10,000 x (1 + 6%)³⁰ = $57,434.91
so he needs to save an additional $237,006.45 - $57,434.91 = $179,571.54

future value of annuity = monthly payment x {[(1 + r)ⁿ - 1]/ r}

monthly payment = future value / {[(1 + r)ⁿ - 1]/ r}

future value = $179,571.54
{[(1 + r)ⁿ - 1]/ r} = {[(1 + 0.005)³⁶⁰ - 1]/ 0.005} = 1,004.515042

monthly payment = $179,571.54 / 1,004.515042 = $178.7644

4 0

3 years ago

The expressions below model different possibilities for the area of a pool. Identify which of the following expressions have at

Anna007 [38]

<h3>Answer: Choice B is correct</h3>

========================================================

Explanation:

Use a graphing tool like GeoGebra, Desmos, or your graphing calculator to plot each expression given as a separate y equation. Four parabolas should result.

The x intercept is the same as the root or zero of a function.

You should find that only choice B has a root thats larger than 4. That specific root being x = 7.

----------------------------

A non-graphing approach:

You can use the quadratic formula or the factoring method to find the roots.

For choice A, it factors to (x+5)(x+6) = 0. The roots are x = -5 and x = -6 which aren't greater than 4. So we cross choice A off the list. Choices C and D are similar stories.

On the other hand, choice B factors to (x-7)(x+2) = 0 and it has roots of x = 7 and x = -2. This is another way to see why choice B is the answer.

Here are the steps for the quadratic formula for choice B

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-14)}}{2(1)}\\\\x = \frac{5\pm\sqrt{81}}{2}\\\\x = \frac{5\pm9}{2}\\\\x = \frac{5+9}{2} \ \text{ or } \ x = \frac{5-9}{2}\\\\x = \frac{14}{2} \ \text{ or } \ x = \frac{-4}{2}\\\\x = 7 \ \text{ or } \ x = -2\\\\$

The quadratic formula is handy in case factoring is either not possible, or guess-and-check is too lengthy of a process. As you can probably tell, we could use the quadratic formula's results to help construct the factored form.

8 0

3 years ago

A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. find the height and radius of the cup that will use the

alekssr [168]

The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
hence the value of x will be:
33=0.262x^3
x^3=125.95
x=(125.95)^(1/3)
x=5.0126=5.01 cm
thus the diameter=height=5.01cm

6 0

4 years ago

Help me please with question 5

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

Winter and summer

8 0

3 years ago

Read 2 more answers

Ali was paid $75 for mowing a neighbor''s yard. This is one fourth of the amount of money she earned all summer

kykrilka [37]

Answer:

75*4= 300. Ali earned $300 that summer

Step-by-step explanation:

5 0

4 years ago