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

$t = 9.9$ years to double

Thanks for the handy formula in poster form.

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

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

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

$ln 2 = 12 t ln(1 + .07/12)$

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

$t approx 9.93$ years

Check:

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