Question 771999
Hello. My name is Joanne. Can you please help me solve this problem? 

A mother wants to invest $14000 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $840, how much moves was invested in the CD?

The answer is $4666.67.

I tried using the formula, A=(1+r/n)^nt, but I am not sure if this is the correct formula to use. Also, I am not sure how to plug in the variables in the formula.


You don’t need the future value formula {{{A = (1 + r/n)^(nt)}}}for this problem, as you’re not calculating TVM (time value of money), or the value of the $14,000 over a certain time period. You’re just trying to determine how much of the $14,000 was invested in  the CD.


As a result, you just simply do the following:


Let amount invested in CD be C
Then amount invested in savings bond = 14,000 – C


Amount of interest earned on the CD, at a 4% interest rate = .04(C), or .04C
Amount of interest earned on the savings bond, at a 7% interest rate = .07(14,000 – C)


Amount of interest earned on CD, plus amount of interest earned on savings bond, equals total interest earned, OR
.04C + .07(14,000 – C) = 840
.04C + 980 - .07C = 840
.04C - .07C = 840 – 980 
- .03C = - 140


C, or amount invested in CD = {{{(- 140)/- .03}}}, or ${{{highlight_green(4667.67)}}}


You can do the check!! 


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