Santiago receives 280 per year in simple interest from three

Santiago receives ?$280 per year in simple interest from three investments. Part is invested at? 2%, part at? 3%, and part at? 4%. There is? $500 more invested at? 3% than at? 2%. The amount invested at? 4% is six times the amount invested at? 3%. Find the amount invested at each rate.

The amount invested at? 2% is

The amount invested at? 3% is

The amount invested at? 4% is

Solution

Let the amounts invested by Santiago at 2 %, 3 % and 4 % be $ x,y,z respectively. Then, y = x+500…(1) and z = 6y …(2). Also, since Santiago receives $ 280 per year in simple interest from the three investments, hence x*0.02+y*0.03+z*0.04 = 280 or, 2x+3y+4z = 28000…(3). Now, on substituting y = x+500 and z = 6y = 6(x+500) = 6x +3000 in the 3^rd equation, we get 2x+3(x+500) +4(6x+3000) = 28000 or, (2x+3x+24x)+ (1500+12000) = 28000 or, 29x = 28000-13500 = 14500 so that x = 14500/29 = 500. Then y = 500+500 = 1000 and z = 6*1000 = 6000. Thus,

The amount invested at 2% is $ 500.

The amount invested at 3% is $ 1000.

The amount invested at 4% is $ 6000.