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8,000 dollars is invested in an account that yields 6% interest per year. After how many years will the account be worth $14 000, to the nearest half year, if the interest is compounded monthly?

Progress

$A = P (1 + i)^n$, so $14 000 = 8 000 (1 + 0.06)^n$, $14 000 = 8 000 (1.06)^n$, $1.75 = (1.06)^n$, $\log 1.75 / \log 1.06 = n$, and so $n = 9.6$ years. Am I correct?

Community
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Immortal
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  • As a starting point, what happens to the investment each month? What is it multiplied by? – turkeyhundt Jan 06 '15 at 02:41
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    How far can you get with this problem before you get stuck? I would set up a formula relating dollars in the account to months that have elapsed, and use that to compute the number of months (rounded to nearest multiple of six). Do you need help understanding how to set up such a formula? Or do you need help understanding how to solve it? – David K Jan 06 '15 at 02:52
  • Yes I need help understanding how to set up the formula. – Immortal Jan 06 '15 at 02:55
  • possible duplicate of Future Values of Annuities – user141592 Jan 06 '15 at 03:23
  • I think I got it.

    A = P (1 + i)^n

    14 000 = 8 000 (1 + 0.06)^n 14 000 = 8 000 (1.06)^n 1.75 = (1.06)^n log 1.75 / log 1.06 = n n = 9.6 years

    Am I correct?

     – Immortal Jan 06 '15 at 03:27
  • I think your equation is solving as if interest is compounded yearly instead of monthly. But your method is correct otherwise. – turkeyhundt Jan 06 '15 at 03:28
  • Please explain why you would use this formula $$A=P(1+i)^n$$ – John Joy Jan 06 '15 at 18:09

2 Answers2

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OK. If you have an annual percentage rate of $6\%$ compounded monthly, that means each month you add $\frac{6\%}{12}$ of the investment to itself.

So each month the investment is multiplied by by $1.005$. ($\text{Investment plus Investment}\times0.005$).

So after $x$ months, your investment is $8000\times(1.005)^x$ Therefore, you need to solve the following equation:$$8000\times(1.005)^x=14000$$

to get the number of months it will take to get to \$14000. I see in your comment above that you know how to solve this. You will have to divide by 12 to get years...

turkeyhundt
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Halfway between 9 and 10 years. Set a formula multiplying the base by 1.06 per year, on the compounding amount.

user201949
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