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 #