Problema Solution
After taxes, Linda decided to invest her $900,000 lottery winnings into two
different accounts. Account A earns 3.5% annual simple interest while account B earns 4%
annual simple interest. At the end of three years the combined interest on her investments was
$100,425.
Write an equation for the total interest earned T (in dollars) from both accounts, in
terms of the amount x invested into account A (recall the simple interest formula given by
I = P rt).
Use your result from a to find the exact amounts invested in each account.
Answer provided by our tutors
Let
x = amount invested into account A at r1 = 0.035 annual simple interest
y = amount invested into account B at r2 = 0.04 annual simple interest
t = 3 years
Linda decided to invest her $900,000 lottery winnings into two different accounts thus
x + y = 900,000
y = 900,000 - x
the total interest earned in 3 years is a sum of the interest from account A and the interest from account B
T = x*r1*t + y*r2*t
T(x) = x*0.035*3 + (900,000 - x)*0.04*3
T(x) = x*(0.105 - 0.12) + 108,000
T(x) = 108,000 - 0.015x is the equation for the total interest earned in 3 years
at the end of three years the combined interest on her investments was $100,425 that is
108,000 - 0.015x = 100,425
x = $505,000
y = 900,000 - 505,000
y = $395,000
Linda invested $505,000 into account A and $395,000 into account B.