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Melody

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यूजर का नामMelody
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Melody  11 Feb 2022
 #1
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Vraces:

I need to understand why for example
[A radioactive kalashnikov gets less radioactive every year. After 60 years only 25% of the radio-activeness remains. What is the yearly reducing of radio-activeness in percent?]

I'm wondering. Since(Based on my assumption) 0.75^(1/60) should be in english: 75% of of the radioactiveness in one year. Since 75% was removed during 60 years shouldn't 0.75^(1/60) be the answer?[1 - 0.25^(1/60) = 0.75^(1/60)? ] And also. Why should it be ^(1/60) and not the percentage divided by 60?What does ^(1/60) actually mean? What happens when it calculates? I'm aware it multiples itself the times stated. For example: 3^3 = 27 ; 3^3(1/3) = 9 I must understand these things. It's good to know how to solve something, but if you don't know the meaning of it you can't solve another thing. I'm going to guess only Melody could explain this, but others are also welcome. IF you actually know the significance. Do not guess while trying to explain as it would only confuse me. And by the way, I may have confused you a little bit with what I'm trying to say. Good luck and thanks.



Hi Vraces,
Firstly I am really glad that you tried to explain. I wish everybody did that.
Your initial problem is very similar to the one you had last time.
Your formula is
S=P(1-r) n
P is present value (or initial value in this case) = P
S is the letter that is usually used for future value = 0.25P
It is -r because the value is getting smaller all the time =unknown
n is number of years = 60

oh I am sorry Vraces I read your response a little wrong. please forgive me, it is after midnight here and I am very tired. i just thought you would appreciate a quick answer.
The 75% that you found is true but it is not relevant to the answer. All that is important is that after 60 years you have 0.25 of your original value.

just use the standard depreciation formula
0.25P=P(1-r) 60 now the p's cancel out
0.25=(1-r) 60

0.25 1/60=1-r [add r to both sides and subtract 0.25 1/60 from both sides.]
r = 1 - 0.25 1/60

this time, the 1 is not in a bracket.
on you calc it is
1- 0.25^(1/60) = 0.022840031 => 2.28% (correct to 3 significant figures)
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Now let me see if i can help you with some of your other issues.

3^2=9 you know that
9^(1/2) means square root of 9 so the answer is 3
so are power of 2 and a power of 1/2 cancel each other out.
sqrt(3 2)=sqrt(9)=3
written in a different way, this is
(3 2) 1/2 = 9 1/2 = 3

2 5 = 2x2x2x2x2 = 32
therefore
32 1/5 = 2
because
32 1/5 means, what times be itself 5 times = 32.

Think about it. If you have more questions post again. You are right, it is important that you understand this.
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I should tell you that we are now fortunate enough to have at least 2 other regular people on the forum who could have helped you with this.
They are reinout-g and I like Serena. I think that some of the others could have helped you too.
But I am glad that I did. I want to keep answering questions for the people I know, especially when I know that they are trying hard to learn.
29 Jan 2014
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AMaqueira3:

Trisha uses her credit card to pay for new tires that ended up totaling $527.89. She can pay off up to $200 a month. The card has an annual rate of 22.5%. How much will she pay in interest?



Hi AMaqueira3 and Reiner-g

Reiner-g, i think that you have made this question more difficult than intended.

Reiner-g has taken 22.5% p.a. to be an effective interest rate whereas I believe it is a nominal annual interest rate.
What Reiner has done is perfectly accurate, it just depends on your interpretation of the question.

I think that the interest rate is a nominal 22.5%pa due monthly. Which means that the effective interest rate is 22.5/12 = 1.875% per month.
1.875% = 0.01875
After that we are in agreement
After 1 month interest
Interest = 0.01875*527.89 = 9.89
Amount owing = original amount + interest = $527.89+9.89 = $537.78
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Instead of doing it in 2 steps like that I could just say that the new amount would be 100% of the original value + another 1.875% of the interest
That is, after 1 month (but before making a payment) you Trisha will owe 101.875% of $527.89 = 1.01875 x $527.89 = $537.78
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so at the end of the 1st month Trisha will owe $537.78 - the $200 payment = $337.78
at the end of th 2nd month Trisha will owe 1.01875*337.78 - 200 = $144.11
work out how much she owes at the end of the 3rd month. Her payment will be less than $200 - she won't owe that much.
Add up how much she paid back take away the original cost and that would have to be the interest.
If not for the difference in the interest rate, Reiner's answer would be the same.
29 Jan 2014