Question 368594
You make a deposit of 2000€ into your account. the interest rate is 5% and the interest is added into the account first after one year and then annually. how long will it take your savings to grow to 10000€ ?
<pre>
{{{A = P(1+r/n)^(nt)}}}

A = Final amount                 = 10000€
P = Beginning amount             = 2000€
r = rate expressed as a decimal  = .05
n = number of compounding/year   = 1 since it is annually (1 time per year)
t = time in years                = what we are to find out.

Substituting:

{{{A = P(1+r/n)^(nt)}}}
{{{10000 = 2000(1+.05/1)^((1)t)}}}
{{{10000 = 2000(1+.05)^t}}}
{{{10000 = 2000(1.05)^t}}}

Divide through by 2000

{{{5 = 1.05^t}}}

Take logarithms (base 10) of both sides:

{{{log(5) = log(1.05^t)}}}

Use the rule of logarithms:  {{{log(B^A) = A*log(B)}}}

{{{log(5) = t*log(1.05)}}}

Divide both sides by {{{log(1.05)}}}

{{{log(5)/log(1.05) = t}}}

Use a calculator:

{{{32.98693374}}}

Answer: 33 years.

Edwin</pre>