# bonds and investing

• Oct 30th 2008, 06:39 AM
mcinnes
bonds and investing
Pat invested \$1200 at the beginning of the year. She used two types of bonds. One at 4% annum another at 6% annum, at the years end she had \$1255. How much did she invest in each bond? Using a system of equations show all of your work.

I get none of this help please.
• Oct 30th 2008, 01:06 PM
HallsofIvy
Quote:

Originally Posted by mcinnes
Pat invested \$1200 at the beginning of the year. She used two types of bonds. One at 4% annum another at 6% annum, at the years end she had \$1255. How much did she invest in each bond? Using a system of equations show all of your work.

I get none of this help please.

You start by assigning names to the things you want to find. You want to find how much she invested in in each bond so we will use "X" to represent the amount of money she invested in the first bond (at 4%) and "Y" to represent the amount of money she invested in the second bond (at 6%).

Now interpret each sentence as an equation. "Pat invested \$1200" gives X+ Y= 1200. X dollars invested at 4% per annum yields .04X in one year and Y dollars invested at 6% per annum yields .06Y in one year. The total yield is .04X+ .06Y. "at the years end she had \$1225" means she had her orginal \$1200 and an additional \$25: .04X+ .06Y= 25.

However, there is a difficulty with this problem! If she had invested all \$1200 dollars at the lower 4%, she would have earned .04(1200)= \$48. Investing some at the higher 6% can't give less than that and 25 is less than 48. I thought perhaps I had misunderstood and she earned the entire 1225 in interest but that is also not possible. If she had invested the full \$1200 dollars at 6% she would have earned .06(1200)= 72 dollars and that's far smaller than 1225. Investing \$1200 split between 4% and 6% must give between \$48 and \$72 interest.
• Oct 31st 2008, 06:44 AM
mcinnes
bro, its \$1255 not \$1225, lol, you miss read it, does that help?