Word problems

Question

 mary inherits 100000 and invests in two certificates or deposits. One certificate pays 6% and the other pays 4.5% simple interest annually. If Marys total interest is 5025 per year, how much money is invested at each rate?

Answer 1

For simple interest, Interest = Principle*Rate*Time , where rate is expressed as a decimal.

 

Let's suppose Mary invests an amount x dollars (of her $100,000) in the 6% certificates. Her interest would after 1 year would be:

 

Interest @ 6% = x*(0.06)*(1 year) = 0.06x

 

Now Mary puts the rest of her money, $100,00-x, into the 4.5% account.  Her interest from that account after 1 year would be:

 

Interest @ 4.5% = (100,00-x)*(0.045)*(1 year) = 4500 - 0.045x

 

Mary's total interest is:

 

Interest = (Interest @ 6%) + (Interest @ 4.5%)

Interest = 0.06x + 4500 - 0.045x

Interest = 0.015x + 4500

 

Since the total interest she earned was $5025:

 

5025 = (0.015)x + 4500

 

525 = (0.015)x

 

Solve for x (amount invested at 6%).  Once you have x, the amount invested at 4.5% is $100,000 - x.