Question 40398
Hello!
The following rules applies for investmentes:

Future Value = Current Value*(1 + r)^n

where r is the interest rate in decimal form (in your case, 6% would be 0.06) and n is the number of periods over which interest is accrued. So we have to find out how many periods (years) it will take for $4,000 to become $10,000. So we solve the equation:

{{{10000 = 4000*(1 + 0.06)^n}}}
{{{10000 = 4000*(1.06)^n}}}

We have to isolate n. In order to do it, we take natural logarithm of both sides:

{{{ln(10000) = ln(4000*(1.06)^n)}}}
{{{ln(10000) = ln(4000) + ln((1.06)^n)}}}
{{{ln(10000) = ln(4000) + n*ln(1.06)}}}
{{{n = (ln(10000)-ln(4000))/ln(1.06)}}}
{{{n = 15.72}}}

si it will take about 15.72 yeras for $4,000 to become $10,000 at a 6% interest rate. Since Ryan was 8 when the investment was made, he will be 23.72 years (almost 24) old when the acct reaches $10,000


I hope this helps!
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