Question

You have invested $11,800 into two different bank accounts. The first account earns 2% interest each year andthe second account earns 5% interest each year. If you earn $453.50 each year in interest, how much was in eachaccount?

Answer 1

Given data:

The total principal amount is x+y=$11,800.

The rate of interest on first amount is r=2%.

The rate of interest on second amount is r'=5%.

The total interest is I=$453.50.

The given timme is t=1 year.

The expression for the total interest is,

$\begin{gathered} I=i+i^{\prime} \\ I=\frac{x\times r\times t}{100}+\frac{y\times r^{\prime}\times t}{100} \end{gathered}$

Substitute the given values in the above expression.

$\begin{gathered} 453.50=\frac{x\times2\times1}{100}+\frac{y\times5\times1}{100} \\ 453.50=0.02x+0.05y \end{gathered}$

Substitute (11,800-x) for y in the above expression.

$\begin{gathered} 453.50=0.02x+0.05(11,800-x) \\ 453.50=0.02x+590-0.05x \\ 0.03x=136.5 \\ x=4,550 \end{gathered}$

The value of y is,

$\begin{gathered} y=11,800-4550 \\ =7,250 \end{gathered}$

The amount in first account is 4,550, and the amount in second account is 7,250.