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`

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}=(P* R* T)/(100)`

For first investment

`I=(x* 12* 1)/(100)\\\\I=0.12x`

For second investment

`II=(\left(20,000-x\right)* 11* 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=(55)/(0.01)\\\\\Rightarrow x=\$5500`

Remaining amount is

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