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Thank you, Grintingriver.
How long does it take to pay off a $125000 mortgage if the annual interest rate is 5.5% and compounded monthly with a monthly payment of $710?
Below is my attempt.
I use the formula
FV = P* ((1+r/n)^(nt)-1)/(r/n)
where FV is future value, r is the interest rate, n is the number of compounding periods in a year, t is the elapsed time, and P is the principal.
12500 = 710*((1+0.055/12)^(12t)-1)/(0.055/12)
Next, I divide both sides by 710 and then multiply both 0.055/12.
3841.24 = (1.0045833333)^(12t)
Then, I take the log of both sides.
log3841.24 = 12t*log1.004583
Lastly, I solve for t and get t = 150 years.
But, the answer key says 30 years.
Can someone explain how to do the problem? Thanks a lot.
Thank you very much for your detailed solution, phrontister. I really appreciate your time and I like your video.
You are a great help.
Thank you very much, bobbym and bob bundy.
I am going to write down a problem below.
(ex) What is the approximate combined loudness in decibels of a garbage disposal truck and a washing machine, each with a sound intensity of 80 decibels?
It looks like a simple problem. I thought the answer was 160 decibels. I got that by multiplying 80 by 2 since the two sounds have the same intensity. But, the answer key says 83 decibels.
Is the answer wrong? Please give me your comments. Thanks.
Thank you very much, bob bundy.
Consider the two functions f(x) = x^2 and g(x) = 1/|x|.
The first one is a parabola with the vertex at the origin. The second one is an absolute value function with a V-shaped graph.
If you take the reciprocal of both functions, their graphs look very similar.
Both have an asymptote along each axis and their curves are in quadrants one and two.
If you just see their reciprocal graphs, how can you tell which graph is represented by which reciprocal function?
Can someone explain this? Thanks a lot.
I am going to write down a problem below.
(ex) Find the points of intersection of r=1-sin(u) and r=1+sin(u) without drawing their graphs.
This is how I do it.
I equate the two equations and get 1-sin(u)=1+sin(u). Simplifying it gives
sin(u)=0. Solving for u gives 0 and pi. Then, the two points are (1 , pi) and (1 , 0).
They are correct. The answer key gives one more answer (0 , pi/2).
How do you find the third answer without graphing? Thanks for your help.
Yes, I now see why there are 30 ones, 30 twos, .... in the ones digit. Shouldn't there be 30 ones, 30 twos, ... in the tens digit as well? Why are there 300 of each in the tens digit?
Hi everyone. I am a new member. I am happy to be part of the forum. Someone solved this problem for me, but I don't understand the steps. I am going to write it down below.
(ex) Determine the sum of all the 3-digit numbers that can be made by choosing 3 different numbers from the list 1, 2, 3, 4, 5, 6, 7.
This is his solution. 30(1+2+3+4+5+6+7) + 300(1+2+3+4+5+6+7) + 3000(1+2+3+4+5+6+7) = (30+300+3000)(28) = 93240.
I have two questions about the solution.
(1) Where do the numbers 30, 300 and 3000 come from?
(2) Why do you have to add up all the whole numbers from 1 to 7?
Could someone please explain the steps to me? Thanks a lot.
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