word problem

Question

$5400 is invested; part of it at 12% and part of it is 9%. For a certain year, the total yield is $576.00. How much was invested at each rate?
How much was invested at 12%?
How much was invested at 9%?

Answer 1

The formula for simple interest is Interest = Principal x Rate x Time

 

In this case, we were given that I = $576, P = $5400, R1 = 12% (0.12), R2 = 9% (0.09), and T = 1 year

 

Let x = amount invested at 12%, then our formula will be

 

$576 = 0.12x + 0.09(5400 - x)

expanding, we get $576 = 0.12x + 486 - 0.09x

combining, we get $90 = 0.03x

solving, we get $3000 = x

 

So, the amount invested at 12% = $3000, leaving $2400 invested at 9%

 

Proof: $3000 x 0.12 + $2400 x 0.09 = $360 + $216 = $576