Figuring point in savings account

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Discussion Overview

The discussion revolves around calculating the time required for an initial savings amount of $20,000 to grow to $1,000,000 at a specified interest rate. Participants explore the application of compound interest formulas and clarify the parameters involved, including the interest rate and compounding frequency.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes using the formula \(20000(1.02)^x = 1000000\) to solve for \(x\), suggesting it leads to approximately 197 months or 16.4 years.
  • Another participant introduces the compound interest formula \(A = P (1 + r/n)^{nt}\) and suggests plugging in values to solve for \(t\).
  • A participant questions the compounding frequency, stating that \(n\) should be 6 if interest is compounded every 2 months, which is contested by others.
  • One participant expresses uncertainty about logarithms and requests assistance from someone knowledgeable in that area.
  • Another participant confirms the original formula was correct and provides a detailed calculation using logarithms, arriving at approximately 198 months or 16.5 years.
  • One participant acknowledges a mistake regarding the interest rate, clarifying it is actually 4% annual instead of 2% per month.

Areas of Agreement / Disagreement

Participants express differing views on the correct interpretation of the interest rate and compounding frequency. There is no consensus on the final calculation, as some participants challenge the assumptions made by others.

Contextual Notes

There are unresolved issues regarding the compounding frequency and the correct interpretation of the interest rate, which may affect the calculations presented.

rock4christ
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say i have an amount of say $20000 in my savings account and at 2% interest per month when will I have 1 million?

my current method is 20000(1.02)x=1000000, and solve for x

I get 197, which is months, 197/12=16.4yr. about. is that right?
 
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I guess what you want is a simple compound interestformula

A = P ( 1 + r/n ) ^nt

Amount is equal to princple times 1 plus rate divided by number of times interest is compounded per year to the numbver of times interest is compounded per year times time.

PLug in your values and solve for t
 
so 1000000=20000(1+0.02/12)nt what answer would you get?
 
Not exactly, n would be 6 because your interest is counted every 2 months .

Also, you have to use the n with the exponent too. After that plug and chug and solve for t. You might have to use logs.
 
thanks, but i don't know logs yet, I am learning them in this unit tho. I was wondering if someone who did know would figure it for me.
 
Bitter said:
Not exactly, n would be 6 because your interest is counted every 2 months .

Also, you have to use the n with the exponent too. After that plug and chug and solve for t. You might have to use logs.
Unless it was editted, I don't see where the original post said anything about "every 2 months".

rock4christ said:
so 1000000=20000(1+0.02/12)nt what answer would you get?
No, that would be for 2% per year and the question is about 2% per month (24% annual- PLEASE tell me where you can get that!). The formula in the orginal post was correct.

[itex]20000(1.02)^x=1000000[/itex]
so [itex]1.02^x= 1000000/20000= 50-[/itex], x log(1.02)= log(50),
x= log(50)/log(102)= 198 months, about 16 and a half years, as the original post said. What was all the fuss about?
 
HallsofIvy said:
Unless it was editted, I don't see where the original post said anything about "every 2 months".


No, that would be for 2% per year and the question is about 2% per month (24% annual- PLEASE tell me where you can get that!). The formula in the orginal post was correct.

[itex]20000(1.02)^x=1000000[/itex]
so [itex]1.02^x= 1000000/20000= 50-[/itex], x log(1.02)= log(50),
x= log(50)/log(102)= 198 months, about 16 and a half years, as the original post said. What was all the fuss about?

ah my mistake, I put the 2 from the 2percent in front of the months. It happens.
 
I was just seeing if my math was right, and its actually 4% annual, I had a bit of a mix up.
 

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