How long will it take for a $400 investment to double if interest is compounded monthly at a rate of 7%? Round to the nearest tenth of a year

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How long will it take for a $400 investment to double if interest is compounded monthly at a rate of 7%? Round to the nearest tenth of a year

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Answer 1 · 2018-05-04T21:28:11

$t = 9.9$ $t = 9.9$ years to double

Explanation:

Thanks for the handy formula in poster form.

$A = P {(1 + \frac{r}{n})}^{n t}$ $A=P(1+r/n)^{nt}$

We have $P = $ 400$ $P=$400$ , $r = .07$ $r=.07$ , $n = 12$ $n=12$ . We want to solve for $t$ $t$ when $A = 2 P$ $A=2P$ which makes the value of $P$ $P$ irrelevant.

$2 P = P {(1 + \frac{.07}{12})}^{12 t}$ $2P = P(1+.07/12)^{12t}$

$ln 2 = 12 t ln (1 + \frac{.07}{12})$ $ln 2 = 12 t ln(1 + .07/12)$

$t = \frac{ln 2}{12 ln (1 + \frac{.07}{12})}$ $t = {ln 2 }/{12 ln(1 + .07/12)}$

$t \approx 9.93$ $t approx 9.93$ years

Check:

$400(1 + .07/12)^{12(9.93)} = 799.947 quad sqrt$

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How long will it take for a $400 investment to double if interest is compounded monthly at a rate of 7%? Round to the nearest tenth of a year

Use this formula for the question.

1 Answer

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