Question 1151563


If you deposit money today in an account that pays {{{4}}}% annual interest, how long will it take to double your money?

Compound interest formula: 

{{{A=P(1+i)^n}}}, where {{{ P}}}=initial investment, {{{i}}}=interest rate per period, {{{A}}}=amount after {{{n}}} periods

{{{A/P=(1+i)^n}}}

For given problem:
{{{n}}}=periods(years)

{{{A=2P}}}, {{{i=.04}}}

{{{2P=P(1+.04)^n}}}
{{{2=(1.04)^n}}}

{{{1.04^n=2}}}

take log of both sides

{{{log(1.04^n)=log(2)}}}

{{{n*log(1.04)=log(2)}}}

{{{n=log(2)/log(1.04)}}}

{{{n }}} ≈{{{17.7 }}}years

ans: It will take {{{17}}} years and {{{8}}} months to double the deposit money