A mother wants to invest 7,000 for education. She invests a portion in a cd which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is$420 how much was invested at each rate?

Question

anonymous · Answer

Let x be the amount invested in the CD account, so (7000 - x) is the amount invested in a savings bond:
 
I = Prt where I = interest earned, P = principal invested, r = rate, and t = time
 
I = 420
 P = 7000
 r1 = 0.04
 r2 = 0.07
 t = 1
 
420 = x(0.04)(1) + (7000 - x)(0.07)(1)
 420 = 0.04x + (7000)(0.07) - 0.07x
 420 = 490 - 0.03x
 0.03x = 490 - 420
 0.03x = 70
 x = 70/0.03
 x = $2333.33