Question

You invest $20,000 in two accounts paying 12% and 11% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $2,255.00.

Answer 1

Answer: $\ 5500, \ 14,500$

Step-by-step explanation:

Given

$\ 20,000$  is invested in two accounts with a 12% and 11% rate of interest.

Total interest after a year is  $\ 2255$

Suppose x amount is invested in first, so the remaining amount is invested in other

Simple interest and Compound interest is the same for a year

$\therefore \text{Interest}=\dfrac{P\times R\times T}{100}$

For first investment

$I=\dfrac{x\times 12\times 1}{100}\\\\I=0.12x$

For second investment

$II=\dfrac{\left(20,000-x\right)\times 11\times 1}{100}\\\\II=0.11\left(20,000-x\right)$

The sum of the two must be $\ 2255$

$\Rightarrow 0.12x+0.11\left (20,000-x\right)=2255\\\Rightarrow 0.01x=2255-2200\\\\\Rightarrow x=\dfrac{55}{0.01}\\\\\Rightarrow x=\ 5500$

Remaining amount is

$\Rightarrow 20,000-5500\\\Rightarrow \ 14,500$