How much did she invest at each rate?

Question

Nina invests $1,750 into two accounts. One account earns 3.5% annual interest and the other earns 4.7% annual interest. At the end of 1 year, Nina earned $73.85 in interest. How much did she invest at each rate?

Answer 1

Since we are only using 1 year, and the interest is compounded

annually (1 time per year) we can use the simple interest formula:

I = prt    Interest = principal(rate)(time)

 

Nina had $1750.  If the invests x amount at 3.5%

then she invests 1750-x in the 4.7% account.

 

Note that the interest rate is expressed as a decimal so

3.5% = .035, 4.7% = .047

 

73.85 = x(.035)(1) + (1750-x)(.047)(1)

73.85 = .035x + 82.25 - .047x

73.85 - 82.25 = -.012x

 

x = -8.4/(-.012) = 700

 

She invested $700 at 3.5% interest

She invested 1785 - 700 = $1,085 at 4.7% interest

 

Hope this helps.  Let me know if you have questions.