SOLUTION: Ryan was 8 when his parents invested $4000 in a certificateof deposite that pays 6% for investments of 3 years. If Ryan leaves the account alone until it reaches $10,000, how old w

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ryan was 8 when his parents invested $4000 in a certificateof deposite that pays 6% for investments of 3 years. If Ryan leaves the account alone until it reaches $10,000, how old w      Log On


   

Question 40398: Ryan was 8 when his parents invested $4000 in a certificateof deposite that pays 6% for investments of 3 years. If Ryan leaves the account alone until it reaches $10,000, how old will he be? ---won't he be 20???
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
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%2A%281+%2B+0.06%29%5En
10000+=+4000%2A%281.06%29%5En
We have to isolate n. In order to do it, we take natural logarithm of both sides:
ln%2810000%29+=+ln%284000%2A%281.06%29%5En%29
ln%2810000%29+=+ln%284000%29+%2B+ln%28%281.06%29%5En%29
ln%2810000%29+=+ln%284000%29+%2B+n%2Aln%281.06%29
n+=+%28ln%2810000%29-ln%284000%29%29%2Fln%281.06%29
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!
Get more answers at Online Math Answers.com!