Here is the question for my homework:

A mother wants to invest $\$7000.00$ for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns $4\%$ and the remainder in a savings bond that earns $7\%$. If the total interest earned after one year is $\$420.00$, how much money was invested in the CD account?

Now, here is my steps:

Amount invested in the savings bond can be represented as $7000 - x$

The interest earned in one year on the CD account is $0.04x$

So, the interest earned on the savings bond in one year can be represented as: $0.07(7000-x)$

The total interested earned after one year is $\$420.00$

The equation is now $0.04x+0.07(7000-x) = 420.00$

Now to SIMPLFY it.

I have this so far

$n - 420 = 0.03x$

How do I get the number $n$?

  • $\begingroup$ Shouldn't your n just be the .07*7000 that you left out in your last line? $\endgroup$ – jericson Oct 3 '10 at 21:24
  • $\begingroup$ @Dan: The solution of your eq. $0.04x+0.07(7000-x)=420.00$ is $x=\frac{7000}{3}\approx 2333.33$. Since the LHS, $0.04x+0.07(7000-x)=490.0-0.03x$, you have the equivalent eq. $490.0-0.03x=420.00$ or $490.0-420.00=0.03x$, the solution of which is $x=\frac{490.0-420.00}{0.03}=\frac{7000}{3}\approx 2333.33$ USD. $\endgroup$ – Américo Tavares Oct 3 '10 at 21:55

I'm not sure what n is supposed to represent but instead of it you should still have that 7000*.07. Now you are left with just a number on the left and you can proceed to solve for x. $$.07(7000)-420.00 = 0.03x$$

  • $\begingroup$ YEs, I got that now. How do you solve this? $\endgroup$ – Dan Oct 3 '10 at 21:31
  • $\begingroup$ I mean what do I do now? $\endgroup$ – Dan Oct 3 '10 at 21:36
  • $\begingroup$ Well you should be able to simplify the left hand side to just a number and so to get x by itself you will then divide both sides by .03. Does this help? If not what are you getting stuck on? From your original question you seem to have a pretty good idea of what is going on and what you need to do. $\endgroup$ – jericson Oct 3 '10 at 21:39
  • $\begingroup$ OK so then I do .07(7000) which gets me 490 and then I do 490-420 which gets me 70 and FINALLY I do 70/.03 which gets me the answer of 2333.33 ! :D $\endgroup$ – Dan Oct 3 '10 at 21:44
  • $\begingroup$ Yes! :) So to summarize she will invest 2333.33 in the CD account and the rest (7000-2333.33) in savings bonds to earn exactly 420 dollars of interest in a year. $\endgroup$ – jericson Oct 3 '10 at 21:47

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