Total annual income of investments was $1257.50 How much was invested at 3% if he invested 2.75% and then invested $4000 twice the amount at 3%

Question

Roberto invested some money at 2.75%, and then invested $4000 more than twice the amount at 3%. His total annual income from the two investments was $1257.50. How much was invested at 3%

Answer 1

Andrew:

 

Let P be Roberto's investment at 2.75%.  At the end of the year he got an annual income (as interest) of

P (0.0275).

 

Assuming that his later investment was at the same time as the first, his other investment at 3%was 4000+2P.  From this investment his annual income(as interest) was (4000 + 2P) (0.03)

 

The total annual income was P (0.0275) + (4000 + 2P) (0.03).  We are given that this amount was 1257.50.

 

Hence

P (0.0275) + (4000 + 2P) (0.03) = 1257.5

 

P [0.0275 + 0.06] + 4000 x 0.03 = 1257.5

 

P (0.0875) + 120 = 1257. 5.   P = (1257.5-120)/0.0875 = 1300.

 

Hence at 3% he invested 4000 + 2x 13000 = 30000.

 

Dattaprabhakar (Dr. G.)