Finding Interest Rates

Question

Jane Hooker invests $40,000 received as an inheritance in three parts. With one part she buys mutual funds that offer a return of 2% per year. The second part, amounts to twice the first, is used to buy government bonds paying 2.5% per year. She puts the rest of the money into a savings account that pays 1.25% annual interest. During the first, year, the total interest is $825. How much did she invest at each rate?

Answer 1

HER Investment in

 

Investment at 2% per year = x

 

Investment at 2.5% per year  = 2x

 

Investment at1.25% per year  = 40,000-(x+2x)=40,000-3x

 

Interest she received from

 

Investment at 2% per year = x*2%= x*0.02 =0.02x

 

Investment at 2.5% per year  = 2x*2.5%=2x*0.025=0.05 x

 

Investment at1.25% per year=(40,000 -3x)* 1.25%= (40,000 -3x)* 0.0125= 500 -0.0375x

 

So

 Total Interest= 825

 

0.02x+0.05x+500-0.0375x=825

 

0.07x-0.0375x+500=825

 

0.0325x =325

 

x=10000

 

Investment at 2% per year = x= $10,000

Investment at 2.5% per year = 2x = 2* 10000=$20,000

Investment at1.25% per year =40,000-3x=40,000-30,000=$10,000