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Thread starter 5 years ago
#1
I have found that after the 5 years both accounts should have the amount 1.298C in them, (I defined C as the initial deposit) however I am not too sure on how I go about finding 'n' from this (when the second account raises to 6%). Any help would be much appreciated!

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5 years ago
#2
(Original post by Black_Materia_)
I have found that after the 5 years both accounts should have the amount 1.298C in them, (I defined C as the initial deposit) however I am not too sure on how I go about finding 'n' from this (when the second account raises to 6%). Any help would be much appreciated!

I'm assuming the simple interest is paid per year?

Call the amount of time that 5% interest is paid and the amount of time 6% is paid .

Then the interest in the first years is and the interest in the next years is so the total amount in the

account after 5 years will be

Can you carry on from here? You're not going to get exactly the same as the compound interest but due to rounding of money, you're looking for and that get you closest to the compound interest.
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Thread starter 5 years ago
#3
(Original post by notnek)
I'm assuming the simple interest is paid per year?

Call the amount of time that 5% interest is paid and the amount of time 6% is paid .

Then the interest in the first years is and the interest in the next years is so the total amount in the

account after 5 years will be

Can you carry on from here? You're not going to get exactly the same as the compound interest but due to rounding of money, you're looking for and that get you closest to the compound interest.
Sorry I'm still not really sure, I did get the same expressions for the total amount and time as you but not sure where to go from those.
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5 years ago
#4
(Original post by Black_Materia_)
Sorry I'm still not really sure, I did get the same expressions for the total amount and time as you but not sure where to go from those.
Setting the compound and simple expressions equal to each other:

So now you need to look for and which satisfy that equation. Since they need to add up to 5, there aren't many choices e.g. 1,4 or 2,3 etc.
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Thread starter 5 years ago
#5
(Original post by notnek)
Setting the compound and simple expressions equal to each other:

So now you need to look for and which satisfy that equation. Since they need to add up to 5, there aren't many choices e.g. 1,4 or 2,3 etc.
From doing that I know that has to be between 2 - 3, and with further calculations between 2 - 2.05, but the exact answer is n = 2.04 years which I'm not sure how to prove without sort of guessing.
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5 years ago
#6
(Original post by Black_Materia_)
From doing that I know that has to be between 2 - 3, and with further calculations between 2 - 2.05, but the exact answer is n = 2.04 years which I'm not sure how to prove without sort of guessing.
How did you get 2-3? And where did you get the answer of 2.04?

I can't see how the answer can be a decimal.
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Thread starter 5 years ago
#7
(Original post by notnek)
How did you get 2-3? And where did you get the answer of 2.04?

I can't see how the answer can be a decimal.
Sorry made a mistake, in order to get close to the the total compound amount then surely t1 will not even be 1 year with t2 > 4, but 2.04 is apparently the answer on my worksheet. I can only assume that the decimal comes from considering daily interest too, so 0.04 would equate to 14 days. But now I am also wondering where 2.04 comes from when 2.04 would give 1.2796C as the total amount which isn't really close to 1.298C..?
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5 years ago
#8
(Original post by Black_Materia_)
Sorry made a mistake, in order to get close to the the total compound amount then surely t1 will not even be 1 year with t2 > 4, but 2.04 is apparently the answer on my worksheet. I can only assume that the decimal comes from considering daily interest too, so 0.04 would equate to 14 days. But now I am also wondering where 2.04 comes from when 2.04 would give 1.2796C as the total amount which isn't really close to 1.298C..?
I don't see how the answer could be 2.04. Either the interest will be payed yearly or monthly (I doubt anything else). How can you switch the type of interest after 2.04 years?
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Thread starter 5 years ago
#9
(Original post by notnek)
I don't see how the answer could be 2.04. Either the interest will be payed yearly or monthly (I doubt anything else). How can you switch the type of interest after 2.04 years?
I'm going to see my tutor tomorrow since I've been puzzled all night over it haha. Thanks for your time and help anyway!
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