value/interest word problem

Question

Meredith invests $1100 in one account and $1600 in an account paying 2 % higher interest. At the end of one year she had earned $248 in interest. At what rates did she invest?

Answer 1

Interest = Principle*Rate*Time

 

For the first account, the principle is $1100.  Let x = the interest rate:

 

Interest = $1100*x*(1 year) = 1100x

 

For the second account, the principle is $1600 and the interest rate is 2% (0.02) higher, so it's x+0.02:

 

Interest = $1600*(x+0.02)*(1year) = 1600x + 32

 

The total interest, $248, is the sum of the two individual interests:

 

$248 = 1100x + 1600x + 32

$216 = 2700x

0.08 = x = 8%

 

The rate on the first account is 8%.  The rate on the second account is x+0.02 = 0.08 + 0.02 = 0.10 = 10%.

 

Check:

$1100*0.08*1 + $1600*0.10*1 = $248

$88 + $160 = $248

$248 = $248

Check!